Finite Group Databasebeta

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C₂²×#2191 #7622832

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

Aliases

Subgroups

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530028);