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C₂×#21307 #6372178

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

Aliases

Subgroups

3574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279374);