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C₂×#45146 #7669625

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

Aliases

Subgroups

8518 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)(10,11)(12,14)(15,16,20,24)(17,21,25,27)(18,22,28,30)(19,26,29,23);(3,4,5,6)(8,11)(12,13)(17,25)(19,29)(21,27)(23,26);(7,9,10,14)(8,12,11,13)(15,17)(16,21)(18,23)(19,22)(20,25)(24,27)(26,28)(29,30);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,18)(16,22)(17,26)(19,27)(20,28)(21,29)(23,25)(24,30);(15,19,20,29)(16,23,24,26)(17,22,25,30)(18,27,28,21)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576821);