Finite Group Databasebeta

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C₂×#20252302 #27080596

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2642 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)(51,59)(53,65)(57,71)(60,68)(61,72)(62,76)(66,67)(77,79);(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)(50,53,55,67,56,65,54,66)(51,58,60,73,59,74,68,78)(52,62,63,77,64,76,69,79)(57,70,72,80,71,81,61,75);(50,52)(51,57)(53,62)(54,69)(55,63)(56,64)(58,70)(59,71)(60,72)(61,68)(65,76)(66,79)(67,77)(73,80)(74,81)(75,78);(50,51,55,60,56,59,54,68)(52,61,63,57,64,72,69,71)(53,58,67,73,65,74,66,78)(62,75,77,70,76,80,79,81);(48,49)

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033886);