Finite Group Databasebeta

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C₂×#7680732 #72298755

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

Aliases

Subgroups

128861 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((8,10)(14,18)(16,17), (4,6)(7,8)(9,10)(14,18)(16,17), (11,12)(13,15)(14,17)(16,18), (4,6)(12,13)(14,18), (3,4)(5,6)(11,13,15,12)(14,17,18,16), (3,4)(5,6)(11,14)(12,16)(13,17)(15,18), (1,2));