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C₂×D₄×#534 #72240961

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

Aliases

Subgroups

154885 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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