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C₂×#12940 #494297

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401493);