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C₂×#508 #3411

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

Aliases

Subgroups

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2143);