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C₂²×#2223 #7622987

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

Aliases

Subgroups

1962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530183);