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C₂²×#3586 #10586993

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

Aliases

Subgroups

56354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10494189);