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C₂×#42590 #7641153

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

Aliases

Subgroups

6036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548349);