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C₂×#20274050 #27365265

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

894 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)(57,62)(59,67)(60,69)(61,68)(63,66)(64,71)(65,70)(72,74,76,81)(73,77,79,86)(75,84,82,80)(78,87,83,85);(56,58)(57,62)(59,69)(60,67)(61,68)(63,71)(64,66)(65,70)(72,73,76,79)(74,77,81,86)(75,83,82,78)(80,87,84,85);(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)(56,57,61,65)(58,66,68,71)(59,64,60,63)(62,69,70,67)(74,80)(75,82)(77,85)(78,83)(81,84)(86,87);(54,55)

Conjugacy classes & character table

1028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 150741);