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C₂²×#2221 #7622985

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

Aliases

Subgroups

2026 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)(8,13)(9,10)(14,29)(15,26)(16,25)(17,27)(19,33)(20,23)(21,22)(24,30)(31,36)(32,35);(5,6,13,26,10,16,22,27,11,17,21,25,9,15,8,12)(7,14,28,29,18,30,33,35,20,31,34,36,23,32,19,24);(5,7)(6,14)(8,19)(9,23)(10,18)(11,20)(12,24)(13,28)(15,32)(16,30)(17,31)(21,34)(22,33)(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, 7530181);