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C₂×#15750 #609397

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

Aliases

Subgroups

3886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,12)(10,11)(13,14)(15,16,19,18)(17,21,22,20)(24,27)(25,29);(8,11)(9,13)(17,22)(20,21)(23,24,26,27)(25,30,29,28);(7,9,10,13)(8,12,11,14)(15,17,19,22)(16,20,18,21)(23,24)(25,28)(26,27)(29,30);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,18,19,16)(17,21,22,20)(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, 516593);