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C₂×#3556 #62760

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

Aliases

Subgroups

3169 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55748);