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C₂²×#2768 #7633535

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

Aliases

Subgroups

7554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540731);