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C₂×#24139 #6448582

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

Aliases

Subgroups

3516 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);(8,11)(12,13)(15,16,20,23)(17,24,27,30)(18,22,19,28)(21,25,29,26);(4,6)(15,17,20,27)(16,21,23,29)(18,26,19,25)(22,30,28,24);(7,9,10,14)(8,12,11,13)(15,18,20,19)(16,22,23,28)(17,25,27,26)(21,24,29,30)

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, 6355778);