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C₂×#11280 #358294

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265490);