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C₂×#23183 #6382751

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

Aliases

Subgroups

3106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(7,8,10,9)(11,12,16,17,15,18,14,20)(13,19,23,24,22,25,21,26);(7,9,10,8)(12,17)(13,21)(14,16)(18,20)(22,23)(24,26);(3,4,5,6)(12,18)(17,20)(19,25)(24,26);(11,13,14,21,15,22,16,23)(12,19,20,26,18,25,17,24)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289947);