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C₂²×#3515 #10585957

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

Aliases

Subgroups

34734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493153);