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C₂×#54953 #8099353

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

Aliases

Subgroups

6390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006549);