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C₂×#45114 #7669624

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

Aliases

Subgroups

8404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576820);