Finite Group Databasebeta

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C₂³×#35350 #72343073

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

Aliases

Subgroups

3518632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

512 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), (8,10)(12,15)(16,18)(21,25)(23,26), (1,2)(3,4)(5,6), (12,15)(16,18), (12,15)(13,17), (7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20,22,24)(21,23,25,26), (11,13)(12,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26));