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C₂×#20276680 #27538032

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 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)(56,58,62,69)(57,64,66,81)(59,68,73,84)(60,74,61,67)(63,76,77,87)(65,80,75,79)(70,83,72,86)(71,85,82,78);(56,57)(58,64)(59,71)(60,65)(61,75)(62,66)(63,70)(67,79)(68,85)(69,81)(72,77)(73,82)(74,80)(76,83)(78,84)(86,87);(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)(57,63)(58,67)(59,70)(60,61)(64,78)(65,82)(66,77)(68,84)(69,74)(71,75)(72,73)(76,79)(80,87)(81,85);(54,55)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 323508);