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C₂×#33580 #7622922

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

Aliases

Subgroups

2312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530118);