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C₂×#11591 #481052

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

Aliases

Subgroups

1082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4,5,7,6,8,9,10)(11,12)(13,22)(14,19)(15,27)(16,31)(17,21)(18,24)(20,29)(23,38)(25,39)(26,37)(28,33)(30,41)(32,36)(34,42)(35,40);(11,13)(12,18)(14,23)(15,28)(16,32)(17,25)(19,33)(20,36)(21,35)(22,27)(24,29)(26,40)(30,42)(31,34)(37,38)(39,41);(11,14,17,16)(12,19,21,31)(13,23,25,32)(15,26,30,29)(18,33,35,34)(20,27,37,41)(22,38,39,36)(24,28,40,42)

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, 388248);