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C₂³×#47826 #72325163

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

Aliases

Subgroups

1570792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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)(12,15)(13,17)(19,20)(21,26)(22,24)(23,25), (11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,23)(25,26), (3,4), (5,6), (7,8,9,10)(13,17)(16,18)(19,20)(21,26)(22,24)(23,25), (1,2)(3,4)(5,6), (11,13)(12,16)(14,17)(15,18)(19,20)(21,24)(22,26)(23,25), (7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,22,23,21)(20,24,25,26));