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C₂×#24295 #6442696

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

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, 6349892);