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C₂×#15610 #609196

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

Aliases

Subgroups

5454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 516392);