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C₂²×#2829 #7633368

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

Aliases

Subgroups

8742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

(1,2);(3,4);(6,9)(10,12)(13,14)(15,18)(16,17)(19,20)(21,22,25,24)(23,26,27,28);(7,11)(10,12)(14,17)(15,19)(22,24)(26,28);(5,6)(7,10)(8,9)(11,12)(13,14)(15,20)(16,17)(18,19)(21,23)(22,26)(24,28)(25,27);(5,7)(6,10)(8,11)(9,12)(13,15,16,19)(14,18,17,20)(21,24,25,22)(23,26,27,28)

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, 7540564);