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C₂×#24422 #6437983

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

Aliases

Subgroups

4500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345179);