Finite Group Databasebeta

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C₂⁴×#534 #72278216

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

Aliases

Subgroups

1140821 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

(3,4)(13,14)(15,17)(16,18)(19,20);(10,12)(13,14,16,18)(15,19,20,17);(15,20)(17,19);(9,10)(11,12)(13,15,16,20)(14,17,18,19);(13,14)(15,19)(16,18)(17,20);(5,6);(7,8);(1,2)(3,4)(5,6)(7,8)

Conjugacy classes & character table

352 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)(13,14)(15,17)(16,18)(19,20), (10,12)(13,14,16,18)(15,19,20,17), (15,20)(17,19), (9,10)(11,12)(13,15,16,20)(14,17,18,19), (13,14)(15,19)(16,18)(17,20), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));