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C₂×#14507 #520892

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

Aliases

Subgroups

4474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428088);