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C₂⁴×#550 #72291239

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

Aliases

Subgroups

914277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

400 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((13,14,17,20)(15,19,16,18), (13,15,17,16)(14,18,20,19), (9,10,11,12)(13,16,17,15)(14,19,20,18), (3,4), (9,10)(11,12)(13,14)(15,18)(16,19)(17,20), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));