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C₂×#12866 #493896

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

Aliases

Subgroups

1306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401092);