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C₂×#3285 #61045

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

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, 54033);