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C₂²×#1796 #6370753

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

Aliases

Subgroups

17018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277949);