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C₂×#47766 #7701743

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

Aliases

Subgroups

8296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7608939);