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C₂×#23562 #6431992

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

Aliases

Subgroups

3414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339188);