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C₂×#56131 #8098790

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

Aliases

Subgroups

6088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8005986);