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C₂³×D₄×H(5,𝔽₂) #72289440

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

Aliases

Subgroups

17328944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 9 generators on 18 points:

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

Conjugacy classes & character table

680 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((11,12,14,16)(13,15,17,18), (11,13)(12,15)(14,17)(16,18), (7,8,10,9)(13,17)(15,18), (8,9)(11,12)(13,15)(14,16)(17,18), (8,9)(11,13)(12,15)(14,17)(16,18), (7,9,10,8)(11,13)(12,15)(14,17)(16,18), (3,4), (5,6), (1,2)(3,4)(5,6));