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C₂×#25890 #6446656

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

Aliases

Subgroups

4970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,13)(10,12)(11,14)(15,16)(17,25)(18,21)(19,24)(20,23)(22,28)(26,29)(27,30);(7,9,11,10)(8,12,14,13)(16,21)(17,26)(19,20)(22,25)(27,28)(29,30);(3,4,5,6)(7,9,11,10)(8,13,14,12)(15,17,20,26,18,27,19,28)(16,22,24,30,21,29,23,25);(7,10,11,9)(8,13,14,12)(16,21)(22,29)(23,24)(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, 6353852);