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C₂×#50175 #7705936

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

Aliases

Subgroups

8658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613132);