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C₂²×#3491 #10585953

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

Aliases

Subgroups

35786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493149);