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C₂×#27675 #6457237

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

Aliases

Subgroups

2180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6364433);