Finite Group Databasebeta

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C₂×#20257131 #27124702

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

7206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 73 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)(58,61,62,70)(59,64,65,69)(60,68,67,73)(63,71,66,72);(60,67)(63,66)(68,73)(71,72);(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)(51,55)(54,57);(50,52,53,56)(51,54,55,57)(58,60)(59,63)(61,68)(62,67)(64,71)(65,66)(69,72)(70,73);(50,51)(52,54)(53,55)(56,57)(58,59,62,65)(60,66,67,63)(61,69,70,64)(68,71,73,72);(48,49)

Conjugacy classes & character table

1238 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1077992);