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C₂×#61208 #10576366

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

Aliases

Subgroups

7834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483562);