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C₂×#34366 #7625974

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

Aliases

Subgroups

9114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533170);