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C₂³×#2312 #72301873

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

Aliases

Subgroups

207221 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((3,4), (5,6), (1,2)(3,4)(5,6), (11,12,14,16)(13,17,18,15)(19,20)(21,25)(22,26)(23,24), (7,8,9,10)(13,18)(15,17)(20,24)(21,26), (11,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,26)(24,25), (11,13)(12,15)(14,18)(16,17)(19,22)(20,21)(23,25)(24,26));