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C₂³×#44936 #72291565

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

Aliases

Subgroups

1806456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

Conjugacy classes & character table

464 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((8,9)(19,20)(21,23)(22,25)(24,26), (7,8,10,9)(13,17)(16,18)(20,21)(22,26), (8,9)(12,15)(16,18), (7,9,10,8)(11,12)(13,16)(14,15)(17,18)(19,21,23,20)(22,25,26,24), (11,13)(12,16)(14,17)(15,18)(19,22)(20,24)(21,25)(23,26), (3,4), (5,6), (1,2)(3,4)(5,6));