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C₂×#16698 #611428

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

Aliases

Subgroups

4342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518624);