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C₂×#120×H(5,𝔽₂) #72298637

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

Aliases

Subgroups

5626954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 18 points:

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

Conjugacy classes & character table

476 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)(12,15)(16,18), (4,6)(8,10), (7,8)(9,10)(13,17)(16,18), (4,6)(7,8,9,10)(11,12)(13,16)(14,15)(17,18), (4,6)(8,10)(11,13)(12,16)(14,17)(15,18), (7,8)(9,10), (3,4)(5,6)(7,8)(9,10), (1,2));