Finite Group Databasebeta

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C₂×#495845 #72320315

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

Aliases

Subgroups

4383 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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