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C₂×#51946 #7707873

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

Aliases

Subgroups

7230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615069);