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C₂×#26492 #6444662

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

Aliases

Subgroups

2402 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)(15,16,20,24)(17,25,27,22)(18,21,28,30)(19,29,26,23);(3,4)(5,6)(8,11)(12,13)(15,17,19,18,20,27,26,28)(16,21,23,25,24,30,29,22);(4,6)(15,17,26,28,20,27,19,18)(16,21,29,22,24,30,23,25);(7,9,10,14)(8,12,11,13)(15,18,19,27,20,28,26,17)(16,22,23,21,24,25,29,30)

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, 6351858);