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C₂²×#2841 #7633367

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

Aliases

Subgroups

7482 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)(13,14,17,18)(15,16,19,20)(23,27)(25,28);(7,11)(10,12)(14,18)(16,20)(21,22,24,26)(23,28,27,25);(5,6)(7,10)(8,9)(11,12)(13,15)(14,16)(17,19)(18,20)(21,23,24,27)(22,25,26,28);(5,7)(6,10)(8,11)(9,12)(13,16)(14,19)(15,18)(17,20)(21,22)(23,25)(24,26)(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, 7540563);