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C₂×#49969 #7705060

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

Aliases

Subgroups

7300 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)(19,20)(21,25)(22,26)(23,24);(3,5)(4,8)(6,9)(7,10)(12,15)(13,17)(19,21,23,26)(20,22,24,25);(5,10)(8,9)(11,12,14,15)(13,16,17,18)(19,20,23,24)(21,25,26,22);(3,5)(4,9)(6,8)(7,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26);(3,6,7,4)(5,8,10,9)(11,13)(12,16)(14,17)(15,18)(19,22)(20,21)(23,25)(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, 7612256);