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C₂×#24109 #6452984

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

Aliases

Subgroups

3504 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)(9,14)(10,12)(11,13)(15,16,18,21)(17,25,27,30)(19,24,20,23)(22,26,29,28);(7,9,11,10)(8,12,13,14)(16,21)(17,26)(19,20)(22,25)(27,28)(29,30);(4,6)(7,10,11,9)(8,12,13,14)(15,17,18,27)(16,22,21,29)(19,26,20,28)(23,30,24,25);(8,13)(12,14)(16,21)(17,27)(23,24)(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, 6360180);