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C₂²×#2574 #7627999

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

Aliases

Subgroups

8266 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)(16,19)(18,20)(21,22,24,26)(23,25,27,28);(14,15)(18,19)(21,22,24,26)(23,25,27,28);(5,6)(7,10)(8,9)(11,12)(13,15,17,14)(16,19,20,18)(21,22)(23,25)(24,26)(27,28);(5,7,8,11)(6,10,9,12)(13,16,17,20)(14,18,15,19)(21,23,24,27)(22,25,26,28)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535195);