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C₂×#135516 #72258362

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

Aliases

Subgroups

3639 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

76 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((4,8,10,16)(5,11)(12,13)(15,17), (3,4,6,8)(5,9,11,15)(7,10,14,16)(12,17,13,18), (3,5,7,13)(4,9,10,18)(6,11,14,12)(8,15,16,17), (1,2));