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C₂×#28182 #6462908

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

Aliases

Subgroups

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6370104);