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C₂³×#2345 #72339230

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

Aliases

Subgroups

117637 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

400 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)(14,18)(16,17)(19,20,22,24)(21,25,26,23), (11,12,15,13)(14,16,18,17)(19,20)(21,23)(22,24)(25,26), (7,9,10,8)(11,13,15,12)(14,16,18,17)(19,20)(21,25)(22,24)(23,26), (3,4), (5,6), (1,2)(3,4)(5,6), (11,14)(12,16)(13,17)(15,18)(19,21)(20,23)(22,26)(24,25));