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C₂×#7312 #128039

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

Aliases

Subgroups

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 35235);