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C₂×#41956 #7640461

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

Aliases

Subgroups

8108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547657);