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C₂×#23427 #6431762

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

Aliases

Subgroups

7322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338958);