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C₂×#35846 #7629460

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

Aliases

Subgroups

8254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536656);