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C₂×#26637 #6439516

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

Aliases

Subgroups

2646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6346712);