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C₂×#7313 #128041

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

Aliases

Subgroups

1404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 35237);