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C₂×#12609 #492957

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

Aliases

Subgroups

1218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400153);