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C₂×#12044 #483497

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

Aliases

Subgroups

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390693);