Finite Group Databasebeta

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C₂×#513003 #72321771

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

Aliases

Subgroups

2385 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

148 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)(5,8)(6,7)(9,10)(11,12)(13,19)(14,21)(15,18)(16,30)(17,31)(20,23)(22,24)(25,35)(26,32)(27,38)(28,34)(29,42)(33,40)(36,41)(37,39), (4,7)(8,10)(12,18)(19,32)(20,33)(21,31)(22,34)(30,42)(35,38)(36,37), (12,19)(13,23)(14,17)(16,24)(18,32)(20,22)(21,38)(25,41)(26,40)(27,39)(28,29)(30,36)(31,35)(33,34)(37,42), (1,2)(11,13,24,41,17,27,29,40,15,26,28,39,14,25,16,23)(12,20,30,35,21,37,34,32,18,33,42,38,31,36,22,19), (3,5,6,9)(4,8,7,10)(11,14,15,17)(12,21,18,31)(13,25,26,27)(16,28,29,24)(19,35,32,38)(20,37,33,36)(22,30,34,42)(23,39,40,41));