Finite Group Databasebeta

?

← Prev (#72325341) Next (#72325343) →

C₂³×#2730 #72325342

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

Aliases

Subgroups

120101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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