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C₂×#20275837 #27411293

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 91 points:

(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(60,63,66,81)(61,68,71,87)(62,73,76,90)(64,80,65,79)(67,82,84,88)(69,86,70,77)(72,85,83,91)(74,78,75,89);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(57,59)(60,62)(61,67)(63,78)(64,75)(65,74)(66,76)(68,85)(69,83)(70,72)(71,84)(73,80)(77,88)(79,90)(81,89)(82,86)(87,91);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(56,57)(58,59)(60,61,66,71)(62,72,76,83)(63,77,81,86)(64,70,65,69)(67,75,84,74)(68,80,87,79)(73,88,90,82)(78,85,89,91);(54,55)

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 196769);