Finite Group Databasebeta

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C₂×#20255191 #27092508

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

2598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 81 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)(50,54)(51,59)(52,64)(53,67)(55,73)(56,70)(57,71)(58,74)(60,78)(61,76)(62,77)(63,79)(65,80)(66,81)(68,75)(69,72);(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)(50,53,57,58)(51,52,62,66)(54,67,71,74)(55,68,56,63)(59,64,77,81)(60,65,61,72)(69,78,80,76)(70,79,73,75);(50,52,57,66)(51,58,62,53)(54,69,71,80)(55,72,56,65)(59,75,77,79)(60,68,61,63)(64,73,81,70)(67,76,74,78);(50,51,57,62)(52,63,66,68)(53,65,58,72)(54,59,71,77)(55,61,56,60)(64,79,81,75)(67,80,74,69)(70,78,73,76);(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1045798);