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C₂²×#3176 #10575298

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

Aliases

Subgroups

7598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482494);