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C₂×#41370 #7639807

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

Aliases

Subgroups

8064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547003);