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C₂×#41446 #7639649

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

Aliases

Subgroups

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546845);