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C₂×#37908 #7635153

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

Aliases

Subgroups

7176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542349);