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C₂×#15054 #608139

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

Aliases

Subgroups

4606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515335);