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C₂×#15722 #609365

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

Aliases

Subgroups

4410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516561);