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C₂×#13493 #499372

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

Aliases

Subgroups

860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

(1,2);(7,8)(9,12)(10,11)(13,14)(15,16,18,22,25,29,30,27,17,20,24,28,19,23,26,21);(3,4)(5,6)(8,11)(12,14)(16,20)(21,27)(22,28)(23,29);(4,6)(7,9,10,13)(8,12,11,14)(16,21)(18,26)(19,25)(20,27)(22,23)(24,30)(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, 406568);