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C₂×#52314 #8092121

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

Aliases

Subgroups

6644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7999317);