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C₂×#36971 #7634340

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

Aliases

Subgroups

7706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541536);