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C₂×#26176 #6438409

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

Aliases

Subgroups

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345605);