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C₂×#13396 #499048

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

Aliases

Subgroups

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406244);