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C₂²×#2742 #7633529

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

Aliases

Subgroups

7874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540725);