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C₂×#35326 #7628612

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

Aliases

Subgroups

7806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535808);