Finite Group Databasebeta

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C₂×#20275266 #27386120

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1670 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)(57,63)(58,67)(60,74)(61,71)(62,75)(64,70)(65,81)(66,72)(68,82)(69,84)(73,83)(76,87)(77,85)(78,79)(80,86);(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)(56,58,66,69,61,68,60,73)(57,62,65,80,64,77,79,76)(59,67,72,84,71,82,74,83)(63,75,81,86,70,85,78,87);(56,57,60,65,61,64,66,79)(58,62,69,76,68,77,73,80)(59,70,72,81,71,63,74,78)(67,75,83,86,82,85,84,87);(54,55)

Conjugacy classes & character table

1202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 171596);