Finite Group Databasebeta

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C₂×#16845 #611618

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

Aliases

Subgroups

4226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 518814);