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C₂×#16895 #611703

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

Aliases

Subgroups

5538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,10,12)(9,13,14,11)(16,19)(20,21)(23,24,26,28)(25,27,30,29);(9,14)(11,13)(15,16,18,19)(17,20,22,21)(23,24)(25,27)(26,28)(29,30);(3,4,5,6)(7,9,10,14)(8,11,12,13)(15,16)(17,21)(18,19)(20,22)(23,24)(25,29)(26,28)(27,30);(7,8)(9,11)(10,12)(13,14)(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, 518899);