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C₂²×#2575 #7628011

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

Aliases

Subgroups

7642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535207);