Finite Group Databasebeta

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C₂³×#2696 #72300203

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

Aliases

Subgroups

126653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(13,17)(16,18)(20,22)(24,25), (7,8)(9,10)(12,15)(16,18)(19,20,23,22)(21,25,26,24), (11,12,14,15)(13,16,17,18)(19,21,23,26)(20,24,22,25), (11,13)(12,16)(14,17)(15,18)(19,22,23,20)(21,24,26,25), (3,4), (5,6), (1,2)(3,4)(5,6));