Finite Group Databasebeta

?

← Prev (#72334696) Next (#72334698) →

C₂×#72334344 #72334697

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

Aliases

Subgroups

902180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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