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C₂³×#36713 #72325326

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

Aliases

Subgroups

1315624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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