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C₂×#59197 #7665836

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

Aliases

Subgroups

7160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573032);