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C₂×#27381 #6450292

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

Aliases

Subgroups

1946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6357488);