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C₂×#20275982 #27411889

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1330 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)(57,59)(60,63,64,76,65,77,80,91)(61,67,68,84,69,74,78,89)(62,71,72,88,73,75,79,90)(66,81,70,86,82,83,85,87);(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)(60,62,65,73)(61,66,69,82)(63,75,77,71)(64,79,80,72)(67,83,74,81)(68,85,78,70)(76,88,91,90)(84,86,89,87);(56,57)(58,59)(60,61,65,69)(62,70,73,85)(63,74,77,67)(64,78,80,68)(66,79,82,72)(71,87,75,86)(76,84,91,89)(81,88,83,90);(54,55)

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 197365);