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C₂×#51746 #7707733

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

Aliases

Subgroups

8502 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)(10,12)(11,14)(16,20)(21,24)(22,27)(28,30);(7,8,10,12)(9,11,14,13)(16,20)(17,23)(18,26)(28,30);(3,4)(5,6)(15,16)(17,24)(18,22)(19,20)(21,23)(25,30)(26,27)(28,29);(7,8)(9,11)(10,12)(13,14)(15,17)(16,21)(18,25)(19,23)(20,24)(22,28)(26,29)(27,30);(7,9)(8,11)(10,14)(12,13)(15,18,19,26)(16,22,20,27)(17,25,23,29)(21,28,24,30)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7614929);