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C₂×#42166 #7640538

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

Aliases

Subgroups

8886 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)(15,16,20,18)(17,21,23,25)(19,22,27,26)(24,28,29,30);(8,11)(12,13)(17,23)(19,27)(21,25)(22,26);(3,4,5,6)(7,8)(9,12)(10,11)(13,14)(15,17)(16,21)(18,25)(19,24)(20,23)(22,28)(26,30)(27,29);(7,9)(8,12)(10,14)(11,13)(15,18,20,16)(17,21,23,25)(19,26,27,22)(24,28,29,30);(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, 7547734);