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C₂×#43501 #7667692

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

Aliases

Subgroups

7702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574888);