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C₂×#36716 #7634018

• 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);(3,4,5,6)(9,13)(12,14)(15,16)(17,24)(18,19)(20,28)(21,23)(22,29)(25,27)(26,30);(8,11)(12,14)(15,17,21,18)(16,19,23,24)(20,25,29,26)(22,27,28,30);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,18,21,17)(16,19,23,24)(20,26,29,25)(22,27,28,30);(7,8)(9,12)(10,11)(13,14)(15,19)(16,17)(18,23)(20,27)(21,24)(22,25)(26,28)(29,30);(7,9)(8,12)(10,13)(11,14)(15,20)(16,22)(17,25)(18,26)(19,27)(21,29)(23,28)(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, 7541214);