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C₂×#37663 #7635025

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

Aliases

Subgroups

8622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542221);