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C₂×#33053 #6629468

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

Aliases

Subgroups

2590 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)(9,12)(10,11)(13,14)(15,16,21,26)(17,23,28,29)(18,22,27,30)(19,25,20,24);(8,11)(12,14)(15,17,19,18,21,28,20,27)(16,22,24,23,26,30,25,29);(7,9,10,13)(8,12,11,14)(15,18,19,28,21,27,20,17)(16,23,24,30,26,29,25,22);(4,6)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536664);