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C₂³×#41955 #72325323

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

Aliases

Subgroups

1365792 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)(21,25)(22,23)(24,26);(8,10)(20,23)(24,25);(3,4);(5,6);(1,2)(3,4)(5,6);(12,15)(16,18)(21,26)(24,25);(7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20)(21,24)(22,23)(25,26);(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,24,23,25)

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