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C₂×#24244 #6442622

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

Aliases

Subgroups

5082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349818);