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C₂×#37315 #7634640

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

Aliases

Subgroups

6254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541836);