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C₂×#20742 #6370970

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

Aliases

Subgroups

4566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278166);