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C₂²×#3173 #10575295

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

Aliases

Subgroups

7166 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)(16,23)(18,24)(20,26)(22,27)(25,28);(6,9)(10,12)(13,14)(15,18)(16,20)(17,19)(21,24)(22,25)(23,26)(27,28);(13,15,16,21,17,22,23,27)(14,18,20,24,19,25,26,28);(5,7,8,11)(6,10,9,12)(14,19)(18,25)(20,26)(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, 10482491);