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C₂×#24475 #6437946

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

Aliases

Subgroups

4575 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345142);