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C₂×#47214 #7700848

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

Aliases

Subgroups

8426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7608044);