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C₂×#3480 #62711

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

Aliases

Subgroups

3901 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55699);