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C₂×#34475 #7626072

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

Aliases

Subgroups

8322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7533268);