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C₂×#22276 #6376420

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

Aliases

Subgroups

3154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283616);