Finite Group Databasebeta

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C₂⁴×#535 #72289435

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

Aliases

Subgroups

1062389 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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