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C₂×#24039 #6440382

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

Aliases

Subgroups

5164 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)(9,12)(10,11)(13,14)(15,16,18,22)(17,24,26,20)(19,21,28,23)(25,30,27,29);(8,11)(12,14)(15,17)(16,20)(18,26)(19,25)(21,29)(22,24)(23,30)(27,28);(4,6)(7,9,10,13)(8,12,11,14)(16,21)(17,25)(19,28)(22,23)(26,27)(29,30);(8,11)(12,14)(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, 6347578);