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C₂×#60970 #10575813

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

Aliases

Subgroups

6690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4)(5,11)(6,10)(7,9)(8,12)(13,17)(14,16)(15,18)(19,20)(21,28)(22,26)(23,25)(24,29)(27,31)(30,33)(32,34);(3,5)(4,8)(6,13)(7,12)(9,11)(10,15)(14,18)(16,17)(19,21,22,29)(20,24,26,28)(23,30,31,34)(25,32,27,33);(5,12)(8,11)(13,18)(15,17)(20,25)(23,31)(24,32)(26,27)(28,33)(30,34);(4,9)(8,11)(10,16)(15,17)(20,26)(24,28)(25,27)(32,33);(3,6,7,14)(4,10,9,16)(5,13,12,18)(8,15,11,17)(20,26)(24,28)(25,27)(32,33)

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, 10483009);