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C₂³×#2691 #72325108

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

Aliases

Subgroups

122557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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