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C₂×#38081 #7635580

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

Aliases

Subgroups

8230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542776);