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C₂×#25019 #6443981

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

Aliases

Subgroups

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351177);