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C₂³×#45448 #72325158

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

Aliases

Subgroups

1348288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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)(13,14)(15,17)(16,18)(19,20)(21,24)(22,26)(23,25), (7,8)(9,10)(11,13,15,18)(12,16,17,14)(19,21,23,26)(20,24,25,22), (3,4), (5,6), (8,10)(19,21)(20,22)(23,26)(24,25), (1,2)(3,4)(5,6), (11,12)(13,16)(14,18)(15,17)(19,21)(20,22)(23,26)(24,25), (7,8)(9,10)(11,14,15,16)(12,13,17,18)(19,22)(20,21)(23,24)(25,26));