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C₂×#53614 #8102598

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

Aliases

Subgroups

6266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,7)(6,8)(9,10)(19,20,22,24)(21,25,26,23);(6,10)(8,9)(11,12)(13,17)(14,15)(16,18)(19,21,22,26)(20,23,24,25);(4,5)(8,9)(12,15)(16,17)(19,21)(20,23)(22,26)(24,25);(3,5,7,4)(6,9,10,8)(11,12)(13,16)(14,15)(17,18)(19,21)(20,23)(22,26)(24,25);(3,6)(4,8)(5,9)(7,10)(11,13)(12,16)(14,18)(15,17)(19,20)(21,23)(22,24)(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, 8009794);