Finite Group Databasebeta

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C₂×#26955 #6443531

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

Aliases

Subgroups

2776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350727);