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C₂×#17586 #6343359

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

Aliases

Subgroups

3308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250555);