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C₂×#45045 #7669472

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

Aliases

Subgroups

6514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576668);