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C₂×#47943 #7703636

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

Aliases

Subgroups

8426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610832);