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C₂×#21623 #6373161

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

Aliases

Subgroups

2560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280357);