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C₂×#45093 #7669623

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

Aliases

Subgroups

11970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576819);