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C₂×#42808 #7641414

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

Aliases

Subgroups

8408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548610);