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C₂×#15043 #608126

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

Aliases

Subgroups

4606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515322);