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C₂×#483836 #72287650

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

Aliases

Subgroups

2645 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 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), (3,4,6,8,7,9,5,10)(12,18,21,33)(13,23)(14,15)(16,31)(19,34,36,32)(20,27,22,38)(24,25)(28,39)(29,30)(35,42,37,41), (11,12,15,18,16,22,14,27,17,21,29,33,31,20,30,38)(13,19,25,32,26,35,28,42,23,36,39,34,40,37,24,41), (11,13)(12,19)(14,28)(15,25)(16,26)(17,23)(18,32)(20,37)(21,36)(22,35)(24,30)(27,42)(29,39)(31,40)(33,34)(38,41), (3,5,7,6)(4,8,9,10)(11,14)(12,20)(13,24)(15,16)(17,30)(18,33)(19,35)(21,22)(23,28)(25,40)(26,39)(29,31)(36,37)(41,42));