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C₂³×#37450 #72339251

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

Aliases

Subgroups

1949656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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