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C₂×#14651 #544303

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

Aliases

Subgroups

6126 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)(12,14)(23,24,26,27)(25,28,30,29);(8,11)(9,13)(16,19)(20,22)(24,27)(28,29);(7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,29)(26,27)(28,30);(7,9)(8,12)(10,13)(11,14)(15,17,18,21)(16,20,19,22)(23,25)(24,28)(26,30)(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, 451499);