Finite Group Databasebeta

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C₂²×#72224639 #72286375

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

Aliases

Subgroups

5795 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 52 points:

(1,2);(3,4);(5,6,8,12,9,13,15,19,10,14,18,7,11,16,20,17)(21,22,24,29,25,31,36,32,26,33,42,44,43,34,41,50)(23,28,37,30,38,27,35,45,40,46,39,49,52,47,51,48);(22,27)(23,35)(24,41)(25,43)(28,31)(29,49)(30,44)(32,45)(33,47)(34,46)(36,42)(37,38)(39,52)(40,51)(48,50);(5,7,15,6,11,19,8,16,10,12,20,14,9,17,18,13)(21,23,36,35,43,52,24,37,26,40,41,51,25,38,42,39)(22,28,32,45,34,47,29,30,33,46,50,48,31,27,44,49)

Conjugacy classes & character table

376 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((1,2), (3,4), (5,6,8,12,9,13,15,19,10,14,18,7,11,16,20,17)(21,22,24,29,25,31,36,32,26,33,42,44,43,34,41,50)(23,28,37,30,38,27,35,45,40,46,39,49,52,47,51,48), (22,27)(23,35)(24,41)(25,43)(28,31)(29,49)(30,44)(32,45)(33,47)(34,46)(36,42)(37,38)(39,52)(40,51)(48,50), (5,7,15,6,11,19,8,16,10,12,20,14,9,17,18,13)(21,23,36,35,43,52,24,37,26,40,41,51,25,38,42,39)(22,28,32,45,34,47,29,30,33,46,50,48,31,27,44,49));