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C₂×#59454 #7665873

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

Aliases

Subgroups

6666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573069);