Finite Group Databasebeta

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C₂×#72233929 #72260643

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

Aliases

Subgroups

3205531 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 30 points:

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

Conjugacy classes & character table

472 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((17,21)(19,22)(23,24,26,28)(25,27,30,29), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(23,24)(25,27)(26,28)(29,30), (3,4,5,6)(11,12)(13,14)(17,21)(19,22)(23,24,26,28)(25,29,30,27), (15,16,18,20)(17,19,21,22)(23,25,26,30)(24,27,28,29), (7,8,9,10)(11,12,13,14)(15,17)(16,19)(18,21)(20,22)(23,24)(25,27)(26,28)(29,30), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)(23,25)(24,27)(26,30)(28,29), (1,2));