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C₂×#33443 #7622585

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

Aliases

Subgroups

1920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529781);