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C₂×#3287 #61047

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

Aliases

Subgroups

1455 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54035);