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C₂×#12770 #493598

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

Aliases

Subgroups

2411 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400794);