Finite Group Databasebeta

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C₉²×#442 #72244155

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 30 points:

(1,2,4,3)(6,9)(7,11)(10,12)(13,14,15,16,17,18,19,20,21);(1,3,4,2)(6,10)(9,12)(22,23,24,25,26,27,28,29,30);(5,6,7,9,8,10,11,12)

Conjugacy classes & character table

1782 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((1,2,4,3)(6,9)(7,11)(10,12)(13,14,15,16,17,18,19,20,21), (1,3,4,2)(6,10)(9,12)(22,23,24,25,26,27,28,29,30), (5,6,7,9,8,10,11,12));