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C₂³×#2473 #72339282

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

Aliases

Subgroups

113045 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((7,8,10,9)(11,12,14,16)(13,17,18,15)(21,24)(22,26), (11,12)(13,15)(14,16)(17,18)(19,20,23,25)(21,22,24,26), (3,4), (5,6), (8,9)(11,12)(13,17)(14,16)(15,18)(19,21)(20,22)(23,24)(25,26), (1,2)(3,4)(5,6), (7,9,10,8)(11,13)(12,15)(14,18)(16,17)(19,22)(20,24)(21,25)(23,26));