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C₂×#3548 #62756

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

Aliases

Subgroups

3905 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55744);