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C₂×#8496 #187396

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

Aliases

Subgroups

2186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94592);