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C₂×#24130 #6448585

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

Aliases

Subgroups

3840 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)(9,13)(10,11)(12,14)(15,16)(17,24)(18,28)(19,23)(20,22)(21,27)(25,30)(26,29);(8,11)(12,13)(15,17,19,27)(16,21,23,24)(18,26,20,25)(22,29,28,30);(4,6)(17,25)(18,20)(21,29)(22,28)(24,30)(26,27);(7,9,10,14)(8,12,11,13)(15,18,19,20)(16,22,23,28)(17,26,27,25)(21,29,24,30)

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, 6355781);