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C₂×#36019 #7629557

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

Aliases

Subgroups

8578 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)(15,16,20,18)(17,21,23,24)(19,22,27,26)(25,28,29,30);(7,8,11,12)(9,13,14,10)(17,23)(21,24)(25,29)(28,30);(3,4)(5,6)(7,9)(8,13)(10,12)(11,14)(15,17)(16,21)(18,24)(19,25)(20,23)(22,28)(26,30)(27,29);(7,10,11,13)(8,9,12,14)(15,18,20,16)(17,24,23,21)(19,22,27,26)(25,28,29,30);(15,19,20,27)(16,22,18,26)(17,25,23,29)(21,28,24,30)

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, 7536753);