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C₂×#15488 #609062

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

Aliases

Subgroups

4714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516258);