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C₂×#26609 #6439399

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

Aliases

Subgroups

2666 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)(17,24)(18,28)(19,23)(20,22)(21,27)(25,30)(26,29);(4,6)(15,17)(16,21)(18,26)(19,27)(20,25)(22,29)(23,24)(28,30);(8,11)(12,14)(17,25)(18,20)(21,29)(22,28)(24,30)(26,27);(4,6)(7,9,10,13)(8,12,11,14)(15,18,19,20)(16,22,23,28)(17,26,27,25)(21,29,24,30)

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, 6346595);