Finite Group Databasebeta

?

← Prev (#72324480) Next (#72324482) →

C₂×#72232045 #72324481

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

Aliases

Subgroups

At least 9400 conjugacy classes of subgroups; only the 39720 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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((11,12)(13,16)(14,15)(17,18)(19,20)(21,25)(22,23)(24,26), (7,8)(9,10)(11,12,14,15)(13,16,18,17)(21,26)(24,25), (11,12)(13,17)(14,15)(16,18), (7,8)(9,10)(12,15)(13,18)(19,21,23,26)(20,24,22,25), (1,2), (4,6)(8,10)(11,12)(13,17)(14,15)(16,18)(19,21)(20,25)(22,24)(23,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,18)(15,17)(19,22,23,20)(21,24,26,25));