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C₂×#24193 #6448781

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

Aliases

Subgroups

3616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6355977);