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C₂³×#2318 #72300218

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

Aliases

Subgroups

129109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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