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C₂²×#3113 #10575075

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

Aliases

Subgroups

7898 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)(13,14,17,20)(15,21,22,28)(16,24,26,19)(18,25,27,23);(6,9)(10,12);(13,15,17,22)(14,18,20,27)(16,25,26,23)(19,28,24,21);(5,7,8,11)(6,10,9,12)(15,22)(18,27)(21,28)(23,25)

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, 10482271);