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C₂×#25372 #6444137

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

Aliases

Subgroups

3214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351333);