Finite Group Databasebeta

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C₂×#4628 #73118

• solvable

Aliases

Subgroups

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 66 points:

(3,12,43,28,21,57,60,63,9,35,41,51,6,30,62,49)(4,16,54,20,32,61,64,8,14,42,52,44,11,37,66,22)(5,27,47,31,39,65,25,13,18,53,45,55,15,48,23,33)(7,36,17,29,46,56,59,26,24,34,40,10,19,58,38,50);(1,2)(7,22,25)(8,23,24)(12,33,36)(13,34,35)(16,40,43)(17,41,42)(19,44,47)(20,45,46)(27,51,54)(28,52,53)(30,55,58)(31,56,57)(37,59,62)(38,60,61)(48,63,66)(49,64,65)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5694);