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C₂×#24335 #6445442

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

Aliases

Subgroups

3616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6352638);