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C₂×#41404 #7639631

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

Aliases

Subgroups

9574 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)(10,11)(12,14)(15,16,20,21)(17,23,26,22)(18,27,29,19)(24,30,28,25);(8,11)(12,13)(16,21)(19,27)(22,23)(25,30);(3,4,5,6)(7,8)(9,12)(10,11)(13,14)(15,17,20,26)(16,22,21,23)(18,28,29,24)(19,25,27,30);(7,9)(8,12)(10,14)(11,13)(15,18)(16,19)(17,24)(20,29)(21,27)(22,30)(23,25)(26,28);(15,19)(16,18)(17,25)(20,27)(21,29)(22,28)(23,24)(26,30)

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, 7546827);