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C₂×#36010 #7629455

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

Aliases

Subgroups

8986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536651);