Finite Group Databasebeta

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C₂×#72231456 #72278698

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

Aliases

Subgroups

2929784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

368 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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