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C₂×#36041 #7629609

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

Aliases

Subgroups

8470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536805);