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C₂×#24050 #6440393

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

Aliases

Subgroups

5050 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)(9,12)(10,11)(13,14)(15,16,20,24)(17,25,27,29)(18,23,19,22)(21,26,30,28);(8,11)(12,14)(17,26)(18,19)(21,29)(22,23)(25,30)(27,28);(4,6)(7,9,10,13)(8,12,11,14)(15,17)(16,21)(18,26)(19,28)(20,27)(22,29)(23,25)(24,30);(8,11)(12,14)(17,27)(21,30)(25,29)(26,28)

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, 6347589);