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C₂×#15788 #609482

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

Aliases

Subgroups

4562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516678);