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C₂×#27598 #6458775

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

Aliases

Subgroups

2216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6365971);