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C₂×#42149 #7640553

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

Aliases

Subgroups

9000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547749);