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C₂×#24219 #6442509

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

Aliases

Subgroups

4848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349705);