Finite Group Databasebeta

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C₂×#20253675 #27084620

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(50,52,53,56)(51,55,54,57)(59,63)(64,70)(65,71)(72,73);(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)(58,60,61,67)(59,64,63,70)(62,69,68,66)(65,72,71,73);(51,54)(55,57)(58,59)(60,64)(61,63)(62,65)(66,73)(67,70)(68,71)(69,72);(50,51)(52,55)(53,54)(56,57)(59,63)(60,66)(62,68)(64,72)(67,69)(70,73);(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1037910);