Finite Group Databasebeta

?

← Prev (#72334697) Next (#72334699) →

C₂×#72297882 #72334698

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

Aliases

Subgroups

At least 6936 conjugacy classes of subgroups; only the 40728 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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((8,10)(11,12)(13,15)(14,17)(16,18)(19,20)(21,24)(22,25)(23,26), (11,13)(12,14)(15,18)(16,17)(19,21)(20,23)(22,26)(24,25), (4,6)(8,10)(11,14)(12,17)(13,18)(15,16), (4,6)(12,18)(14,15)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,8,9,10)(11,15,16,14)(12,13,18,17)(19,20)(21,23)(22,25)(24,26), (1,2), (11,13)(12,15)(14,18)(16,17));