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C₂×#1747 #20369

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

Aliases

Subgroups

465 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13357);