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C₂×#23693 #6432262

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

Aliases

Subgroups

2612 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)(9,12)(10,11)(13,14)(15,16)(17,23)(18,21)(19,22)(20,25)(24,30)(26,29)(27,28);(8,11)(12,14)(17,24)(19,26)(20,28)(22,29)(23,30)(25,27);(4,6)(15,17,18,25)(16,20,21,23)(19,27,26,24)(22,30,29,28);(7,9,10,13)(8,12,11,14)(16,21)(20,23)(22,29)(28,30)

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, 6339458);