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C₂²×#2180 #7622629

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

Aliases

Subgroups

1918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(1,2);(3,4);(5,6)(7,17,19,28)(8,21)(9,13)(10,25)(11,16)(12,18,29,35)(14,22)(15,27)(20,32,26,34)(23,33,36,30)(24,31);(5,7)(6,12)(8,18)(9,23)(10,26)(11,19)(13,28)(14,32)(15,33)(16,29)(17,31)(20,27)(21,34)(22,35)(24,36)(25,30);(5,8,10,9,11,22,27,24)(6,13,15,21,16,31,25,14)(7,18,26,23,19,35,20,36)(12,28,33,34,29,17,30,32)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529825);