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C₂×#42683 #7641334

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

Aliases

Subgroups

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548530);