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C₂²×#3566 #10586142

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

Aliases

Subgroups

32622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 36 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493338);