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C₂×#12904 #494151

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

Aliases

Subgroups

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401347);