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C₂²×#2569 #7628008

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

Aliases

Subgroups

8994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535204);