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C₂×#16099 #610108

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

Aliases

Subgroups

3918 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)(15,16,18,19)(17,21,22,20)(23,24)(25,29)(26,28)(27,30);(8,11)(12,14)(16,19)(17,22)(23,24,26,28)(25,29,30,27);(7,8,10,11)(9,12,13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,27)(26,28)(29,30);(3,4)(5,6)(7,9)(8,12)(10,13)(11,14)(15,17,18,22)(16,20,19,21)(23,25,26,30)(24,27,28,29)

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, 517304);