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C₂×#2409 #34682

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

Aliases

Subgroups

2783 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27670);