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C₂×#14899 #607896

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

Aliases

Subgroups

4050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(9,13)(12,14)(15,16)(17,19)(18,21)(20,22)(23,24,26,28)(25,29,30,27);(8,11)(12,14)(16,17)(20,21)(23,24,26,28)(25,27,30,29);(7,8)(9,12)(10,11)(13,14)(15,17,19,16)(18,21,22,20)(23,24)(25,27)(26,28)(29,30);(3,4)(5,6)(7,9,10,13)(8,12,11,14)(15,18,19,22)(16,20,17,21)(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, 515092);