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C₂×#8491 #187390

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

Aliases

Subgroups

2662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94586);