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C₂×#23896 #6437627

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

Aliases

Subgroups

6306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344823);