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C₂×#2155 #33403

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

Aliases

Subgroups

329 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26391);