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C₂×#3155 #60641

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

Aliases

Subgroups

1767 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53629);