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C₂×#42812 #7641430

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

Aliases

Subgroups

8322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548626);