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C₂×#12975 #494395

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

Aliases

Subgroups

1097 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401591);