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C₂×C₄×#553 #7625396

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

Aliases

Subgroups

9266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532592);