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C₂×#24830 #6445544

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

Aliases

Subgroups

2656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6352740);