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C₂×#45095 #7669644

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

Aliases

Subgroups

8372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576840);