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C₂×#25048 #6444062

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

Aliases

Subgroups

2596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6351258);