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C₂×#44438 #7668405

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

Aliases

Subgroups

6336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575601);