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C₂×#14619 #521138

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

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, 428334);