Finite Group Databasebeta

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C₂²×#13269 #72307529

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

Aliases

Subgroups

5297 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(1,2);(3,4);(6,11)(7,16,18,29)(9,22)(12,24,17,25)(13,15)(19,33,32,30)(20,34)(26,36,31,35);(1,2)(3,4)(5,6,10,11)(7,17)(8,15,21,13)(9,14,22,23)(12,18)(16,25)(19,31)(20,28,34,27)(24,29)(26,32)(30,36)(33,35);(5,7,9,19,8,16,20,30,10,18,22,32,21,29,34,33)(6,12,14,26,15,24,28,35,11,17,23,31,13,25,27,36)

Conjugacy classes & character table

184 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((1,2), (3,4), (6,11)(7,16,18,29)(9,22)(12,24,17,25)(13,15)(19,33,32,30)(20,34)(26,36,31,35), (1,2)(3,4)(5,6,10,11)(7,17)(8,15,21,13)(9,14,22,23)(12,18)(16,25)(19,31)(20,28,34,27)(24,29)(26,32)(30,36)(33,35), (5,7,9,19,8,16,20,30,10,18,22,32,21,29,34,33)(6,12,14,26,15,24,28,35,11,17,23,31,13,25,27,36));