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C₂×#33038 #6629419

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

Aliases

Subgroups

2840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6536615);