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C₂×#37841 #7635311

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

Aliases

Subgroups

8800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542507);