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C₂×#15995 #609942

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

Aliases

Subgroups

4594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 517138);