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C₂×#3270 #61028

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

Aliases

Subgroups

1371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54016);