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C₂×#11922 #483035

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

Aliases

Subgroups

1108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390231);