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C₂×#11584 #481043

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

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, 388239);