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C₂×#24090 #6452966

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

Aliases

Subgroups

3628 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)(16,21)(17,25)(18,20)(22,26)(27,28)(29,30);(7,9,11,10)(8,12,13,14)(15,16,19,21)(17,26,28,30)(18,23,20,24)(22,25,29,27);(4,6)(7,10,11,9)(8,12,13,14)(15,17,19,28)(16,22,21,29)(18,27,20,25)(23,30,24,26);(8,13)(12,14)(15,18,19,20)(16,23,21,24)(17,27,28,25)(22,30,29,26)

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, 6360162);