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C₂×#3289 #61099

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

Aliases

Subgroups

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54087);