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C₂³×#38020 #72339215

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

Aliases

Subgroups

1948584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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