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C₂×#33744 #7623238

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

Aliases

Subgroups

1436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530434);