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C₂×#12648 #493076

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

Aliases

Subgroups

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,11,16)(9,19)(10,25,12,28)(13,30,26,18)(14,22)(15,29,17,27)(20,35)(21,34)(23,38)(24,32)(31,36)(33,37);(4,6)(7,9,12,22,13,23,29,36,11,24,10,21,26,20,27,37)(8,14,17,32,18,33,28,38,16,34,15,19,30,31,25,35);(9,20,24,23)(10,12)(14,31,34,33)(15,17)(19,35,32,38)(21,37,22,36)(25,28)(27,29)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400272);