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C₂×#2364 #34137

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

Aliases

Subgroups

2131 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)(13,17)(14,15)(16,18);(7,9,10,8)(12,15)(16,17);(3,4,5,6)(11,13)(12,16)(14,18)(15,17);(11,12)(13,16)(14,15)(17,18)

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, 27125);