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C₂×#12079 #483799

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

Aliases

Subgroups

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390995);