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C₂²×#2193 #7622842

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

Aliases

Subgroups

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530038);