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C₂²×#3544 #10586149

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

Aliases

Subgroups

34538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493345);