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C₂×#8809 #191375

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

Aliases

Subgroups

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 98571);