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C₂×#8524 #187804

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

Aliases

Subgroups

3214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 95000);