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C₂×#45134 #7669586

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

Aliases

Subgroups

11900 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)(11,12,16,20)(13,17,21,23)(14,18,24,26)(15,22,25,19);(4,6)(13,21)(15,25)(17,23)(19,22);(7,8,9,10)(11,13)(12,17)(14,19)(15,18)(16,21)(20,23)(22,24)(25,26);(3,4)(5,6)(11,14)(12,18)(13,22)(15,23)(16,24)(17,25)(19,21)(20,26);(11,15,16,25)(12,19,20,22)(13,18,21,26)(14,23,24,17)

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, 7576782);