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C₂×#23640 #6432179

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

Aliases

Subgroups

3166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(7,8)(9,12)(10,11)(13,14)(15,16,20,22,19,24,18,23)(17,21,27,28,25,29,26,30);(3,4)(5,6)(8,11)(12,14)(15,17)(16,21)(18,26)(19,25)(20,27)(22,28)(23,30)(24,29);(4,6)(7,9,10,13)(8,12,11,14)(16,22)(18,20)(21,28)(23,24)(26,27)(29,30);(17,25)(21,29)(26,27)(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, 6339375);