Finite Group Databasebeta

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C₂³×#2812 #72300214

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

Aliases

Subgroups

224677 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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