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C₂×#3141 #60616

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

Aliases

Subgroups

1199 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

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, 53604);