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C₂×#44447 #7668807

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

Aliases

Subgroups

11466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576003);