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C₂×#21841 #6374361

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

Aliases

Subgroups

4258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,5,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,23)(18,21)(19,22)(20,25)(24,29)(26,28)(27,30);(8,11)(12,13)(15,17,19,25)(16,20,22,23)(18,26,27,24)(21,29,30,28);(8,12)(10,14)(11,13)(15,18,19,27)(16,21,22,30)(17,24,25,26)(20,28,23,29);(8,11)(12,13)(16,22)(20,23)(21,30)(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, 6281557);