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C₂²×#2493 #7627914

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

Aliases

Subgroups

8690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535110);