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C₂²×#3552 #10586145

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

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, 10493341);