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C₂²×#2494 #7627950

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

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, 7535146);