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C₂×#16098 #610107

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

Aliases

Subgroups

3194 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)(17,20)(18,19)(21,22)(24,27)(25,29);(8,11)(12,14)(16,19)(17,21)(23,24,26,27)(25,30,29,28);(7,8,10,11)(9,12,13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30);(3,4)(5,6)(7,9)(8,12)(10,13)(11,14)(15,17,18,21)(16,20,19,22)(23,25,26,29)(24,28,27,30)

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, 517303);