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C₂×#22459 #6379188

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

Aliases

Subgroups

4550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6286384);