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C₂×#16884 #611691

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

Aliases

Subgroups

5386 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)(16,19)(20,21)(23,24,26,28)(25,27,30,29);(8,11)(12,14)(15,16,18,19)(17,20,22,21)(23,24)(25,27)(26,28)(29,30);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16)(17,21)(18,19)(20,22)(23,24)(25,29)(26,28)(27,30);(7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,22)(19,21)(23,25)(24,27)(26,30)(28,29)

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, 518887);