Finite Group Databasebeta

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C₂×C₅²×#347 #72253200

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

1100 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((3,4,5,10,6,8,12,15,7,9,11,16,13,14,18,17)(19,20,21,22,23), (1,2)(24,25,26,27,28), (4,8,9,14)(5,11)(10,17,16,15)(12,18));