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C₂×#24973 #6446995

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

Aliases

Subgroups

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6354191);