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C₂×#3266 #61024

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

Aliases

Subgroups

1441 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54012);