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C₂×#38485 #7635901

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

Aliases

Subgroups

5842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543097);