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C₂×#3278 #61037

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

Aliases

Subgroups

1397 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54025);