Finite Group Databasebeta

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C₂³×#2709 #72300205

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

Aliases

Subgroups

141893 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((8,10)(11,12,15,17)(13,14,16,18)(21,25)(23,26), (7,8)(9,10)(19,20,22,24)(21,26,25,23), (11,13)(12,14)(15,16)(17,18)(19,20)(21,23)(22,24)(25,26), (11,14)(12,16)(13,17)(15,18)(19,21)(20,23)(22,25)(24,26), (3,4), (5,6), (1,2)(3,4)(5,6));