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C₂×#58880 #8105086

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

Aliases

Subgroups

6486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8012282);