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C₂×#15791 #609485

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

Aliases

Subgroups

3314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516681);