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C₂×#25575 #6449029

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

Aliases

Subgroups

4008 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)(10,11)(12,14)(15,16)(17,23)(18,21)(19,22)(20,25)(24,29)(26,28)(27,30);(8,11)(12,13)(15,17)(16,20)(18,25)(19,24)(21,23)(22,28)(26,27)(29,30);(3,4,5,6)(17,24)(19,27)(20,28)(22,30)(23,29)(25,26);(7,9,10,14)(8,12,11,13)(16,21)(20,23)(22,30)(28,29)

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, 6356225);