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C₂³×#43546 #72325313

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

Aliases

Subgroups

1312096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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)(16,18)(20,23)(24,26), (12,15)(13,17)(19,20)(21,24)(22,23)(25,26), (3,4), (5,6), (8,10)(13,17)(16,18), (1,2)(3,4)(5,6), (7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20)(21,24)(22,23)(25,26), (7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,21,22,25)(20,24,23,26));