Finite Group Databasebeta

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C₂×#483597 #72255408

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

Aliases

Subgroups

2925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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