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C₂²×#2832 #7633375

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

Aliases

Subgroups

8018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540571);