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C₂×#36705 #7634017

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

Aliases

Subgroups

8854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541213);