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C₂×#26906 #6439644

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

Aliases

Subgroups

2542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6346840);