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C₂×#22207 #6376209

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

Aliases

Subgroups

2382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283405);