The team comprises 18 non-commissioned officers at the state level
At the close Bangladesh, replying to England’s 599 for six declared, were struggling at 154 for five with only opener Tamin Iqbal standing firm.
Tamim was unbeaten on 81 after Paul Collingwood had collected his 10th test century to enable England to declare their first innings at 599 for six.
Facing an uphill task to avoid the follow-on, Bangladesh suffered an early setback when fast bowler Broad dismissed opener Imrul Kayes (4) and Junaid Siddique (7) with short-pitched deliveries before Swann continued his remarkable record of capturing a wicket in his opening over.
Swann had Aftab Ahmed (1) caught by Ian Bell at leg-slip to give the off-spinner a wicket with his fifth ball after the tea break and reduce Bangladesh to 51 for three.
Tamim then shared a 94-run partnership with Mahmudullah (51) to repair the damage before Swann struck again.
Mahmudullah, who had raced to his fifty off 54 balls with seven cleanly struck boundaries and a six, attempted a sweep shot but managed only to glove the ball to Collingwood at slip.
Skipper Shakib Al Hasan survived some anxious moments before he was bowled by Swann for one attempting do drive.
Swann could have added another wicket but nightwatchman Shahadat Hossain was given the benefit of the doubt by the third umpire in the same over when England appealed for a catch at silly point.
Collingwood, 32 not out overnight, punished the innocuous Bangladesh bowling with 145 from 188 balls.
He completed his century with a single off Shahadat and Ian Bell, his partner in the 184-run fifth wicket stand, drove the next ball to the cover boundary to bring up his fifty.
Collingwood, who hit 10 fours and four sixes, had one let off in his innings when Shakib dropped a return catch when the batsman was on 119.
Wicketkeeper Mushfiqur Rahim fumbled a chance off Bell when the batsman was on 64 off Razzak and he was again dropped by Rubel Hossain off Shakib. Rubel made amends for his mistake with the next ball to catch Bell for 84 and Alastair Cook declared the innings immediately.
Earlier, Cook fell short of a double century when off-spinner Mahmudullah had him caught and bowled for 173 in the 13th over of the morning.
Cook, resuming on 158 not out, eased past his previous career best of 160 but an attempted pull shot caught the leading edge and Mahmudullah took a simple catch. Cook struck 16 fours and two sixes in his 283-ball knock.
England, put into bat, ended the opening day on 374-3 with former skipper Kevin Pietersen contributing 99 runs.
The team comprises 18 non-commissioned officers at the state level
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