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C₂×#40589 #7638902

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

Aliases

Subgroups

8430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546098);