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C₂×#16647 #611258

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

Aliases

Subgroups

4830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518454);