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C₂×#16699 #611429

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

Aliases

Subgroups

4342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(8,11)(12,13)(15,16,18,20)(17,21,22,19)(24,27)(25,29);(7,8,10,11)(9,12,14,13)(15,16)(17,19)(18,20)(21,22)(23,24)(25,30)(26,27)(28,29);(3,4,5,6)(7,8)(9,13)(10,11)(12,14)(15,16)(17,21)(18,20)(19,22)(23,25)(24,28)(26,29)(27,30);(7,9)(8,12)(10,14)(11,13)(15,17)(16,19)(18,22)(20,21)(23,24)(25,30)(26,27)(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, 518625);