Finite Group Databasebeta

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C₂³×#2661 #72325111

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

Aliases

Subgroups

135341 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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