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C₂×#15756 #609404

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

Aliases

Subgroups

4930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516600);