Finite Group Databasebeta

?

← Prev (#72240959) Next (#72240961) →

C₂×#7684300 #72240960

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

Aliases

Subgroups

At least 7668 conjugacy classes of subgroups; only the 34573 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

(3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18);(4,5)(7,8,9,10)(11,12,14,15)(13,16,17,18);(8,10)(12,15)(16,18);(13,17)(16,18);(3,5,6,4)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18);(1,2);(11,13)(12,16)(14,17)(15,18)

Conjugacy classes & character table

226 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((3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18), (4,5)(7,8,9,10)(11,12,14,15)(13,16,17,18), (8,10)(12,15)(16,18), (13,17)(16,18), (3,5,6,4)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18), (1,2), (11,13)(12,16)(14,17)(15,18));