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C₂²×#3290 #10576165

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

Aliases

Subgroups

10342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 36 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483361);