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C₂×#484139 #72287147

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

Aliases

Subgroups

2289 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 50 points:

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

Conjugacy classes & character table

124 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)(5,8)(6,10)(7,9)(11,15)(12,14)(13,16)(17,18)(19,20)(21,27)(22,28)(23,37)(24,30)(25,29)(26,31)(32,42)(33,41)(34,43)(35,44)(36,45)(38,49)(39,47)(40,46)(48,50), (19,21,25,32,24,34,40,48,26,33,23,38,39,22,35,36)(20,27,29,42,30,43,46,50,31,41,37,49,47,28,44,45), (3,5,6,11,7,12,13,17)(4,8,10,15,9,14,16,18)(19,22,24,33,26,34,39,21)(20,28,30,41,31,43,47,27)(23,38,35,48,25,32,40,36)(29,42,46,45,37,49,44,50), (4,9)(8,14)(10,16)(15,18)(19,23)(20,29)(22,34)(24,40)(25,26)(27,41)(30,44)(31,37)(32,36)(35,39)(38,48)(42,50)(45,49)(46,47));