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C₂×#3557 #62738

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

Aliases

Subgroups

3277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55726);