Finite Group Databasebeta

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C₂×#564⋊C₃ #85658

• solvable
• monomial

Aliases

Splittings

Subgroups

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 48 points:

(1,7,11,2,3,21)(4,22,27,8,12,38)(5,24,32,9,14,42)(6,26,28,10,19,39)(13,40,18,23,29,25)(15,33,46,17,31,47)(16,37,43,20,35,48)(30,45,34,41,44,36);(1,25)(2,18)(3,19,7,26)(4,36)(5,6)(8,34)(9,10)(11,42,21,32)(12,35,22,37)(13,24,23,14)(15,16)(17,20)(27,47,38,46)(28,40,39,29)(30,33,41,31)(43,45,48,44);(3,12,7,22)(6,10)(11,38,21,27)(13,41,23,30)(14,33,24,31)(16,20)(18,25)(19,35,26,37)(28,43,39,48)(29,45,40,44)(32,46,42,47)(34,36)

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18234);