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C₂³×#2459 #72300213

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

Aliases

Subgroups

134269 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

304 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)(11,12,14,16)(13,17,18,15)(19,20,24,23)(21,26,22,25), (7,8)(9,10)(19,21,24,22)(20,25,23,26), (11,13,14,18)(12,15,16,17)(19,22,24,21)(20,26,23,25), (11,12)(13,17)(14,16)(15,18)(19,23,24,20)(21,26,22,25), (3,4), (5,6), (1,2)(3,4)(5,6));