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C₂×#61291 #10576597

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

Aliases

Subgroups

6614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483793);