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C₂×#14613 #521116

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 428312);