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C₂×#16886 #611693

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

Aliases

Subgroups

4862 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)(17,18)(19,20)(21,22)(24,27)(28,29);(8,11)(12,14)(16,20)(17,22)(23,24,26,27)(25,28,30,29);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,17)(16,21)(18,20)(19,22)(23,24)(25,29)(26,27)(28,30);(7,9)(8,12)(10,13)(11,14)(15,18,19,21)(16,22,20,17)(23,25,26,30)(24,28,27,29)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 518889);