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C₂×#31245 #7503879

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

Aliases

Subgroups

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411075);