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C₂×#12549 #492844

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400040);