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C₂×#61444 #10576757

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

Aliases

Subgroups

7188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483953);