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C₂×#37700 #7635125

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

Aliases

Subgroups

8804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542321);