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C₂×#37547 #7633808

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

Aliases

Subgroups

8974 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)(18,26)(21,28)(24,30)(27,29);(8,11)(12,13)(15,16,19,22)(17,20,25,23)(18,21,26,28)(24,27,30,29);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16)(17,23)(18,21)(19,22)(20,25)(24,29)(26,28)(27,30);(7,9,10,14)(8,12,11,13)(15,17)(16,20)(18,24)(19,25)(21,27)(22,23)(26,30)(28,29);(15,18)(16,21)(17,24)(19,26)(20,27)(22,28)(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, 7541004);