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C₂×#47800 #7701865

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

Aliases

Subgroups

7746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7609061);