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C₂×#8494 #187394

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

Aliases

Subgroups

2370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 94590);