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C₂×#2325 #34066

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

Aliases

Subgroups

2075 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27054);