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C₂×#2049 #23524

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

Aliases

Subgroups

661 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

46 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 16512);