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C₂×#44784 #7669178

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

Aliases

Subgroups

7556 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)(9,10)(11,13)(12,14)(18,26)(22,27)(24,30)(28,29);(7,9,12,11)(8,13,14,10)(16,20)(18,26)(21,23)(24,30);(3,4)(5,6)(15,16,19,20)(17,23,25,21)(18,22,26,27)(24,29,30,28);(7,10,12,13)(8,9,14,11)(15,17,19,25)(16,21,20,23)(18,24,26,30)(22,28,27,29);(7,11,12,9)(8,13,14,10)(15,18)(16,22)(17,24)(19,26)(20,27)(21,28)(23,29)(25,30)

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, 7576374);