Finite Group Databasebeta

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C₂×#17142 #844918

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

Aliases

Subgroups

3974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 752114);