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C₂×#16006 #609955

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

Aliases

Subgroups

4442 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)(17,20,21,22)(23,24)(25,30)(26,27)(28,29);(8,11)(12,14)(16,19)(17,21)(23,25,28,26)(24,27,29,30);(7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,26,28,25)(24,27,29,30);(3,4)(5,6)(7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,21)(19,22)(23,27)(24,25)(26,29)(28,30)

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, 517151);