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C₂×#16036 #609989

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

Aliases

Subgroups

3918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 517185);