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C₃²×H(7,𝔽₂) #11770643

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

17976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2,3)(7,8)(9,13)(10,17)(11,12)(14,18)(15,19)(16,22)(20,21);(4,5,6)(8,12)(13,19)(14,17)(20,22);(9,15)(13,19)(16,21)(20,22);(7,9)(8,13)(10,16)(11,15)(12,19)(14,20)(17,22)(18,21);(7,8)(9,13)(10,14)(11,12)(15,19)(16,20)(17,18)(21,22);(7,10)(8,14)(9,16)(11,18)(12,17)(13,20)(15,21)(19,22)

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4654);