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C₂×#27662 #6457144

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6364340);