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C₂×#2145 #33387

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

Aliases

Subgroups

585 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 26375);