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C₂×#11284 #358301

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

Aliases

Subgroups

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 265497);