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C₂×#20276595 #27537491

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

662 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)(56,59,61,73,62,74,77,60)(57,64,65,82,67,83,66,75)(58,69,70,78,72,86,71,76)(63,79,80,85,81,87,84,68);(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)(56,58)(57,63)(59,69)(60,76)(61,70)(62,72)(64,79)(65,80)(66,84)(67,81)(68,75)(71,77)(73,78)(74,86)(82,85)(83,87);(56,57,61,65,62,67,77,66)(58,68,70,79,72,85,71,87)(59,64,73,82,74,83,60,75)(63,78,80,86,81,76,84,69);(54,55)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322967);