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C₂×#13502 #499389

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

Aliases

Subgroups

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406585);