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C₂×#23965 #6451791

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

Aliases

Subgroups

4446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6358987);