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C₂×#34974 #7628148

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

Aliases

Subgroups

6474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535344);