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C₂×#8495 #187395

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

Aliases

Subgroups

2002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 50 points:

(1,2);(4,8,10,13)(9,17,18,16)(19,20)(21,29,32,25)(22,33,35,42)(23,28)(24,27)(26,34,40,36)(30,45)(31,44,49,39)(37,41)(38,46)(43,48)(47,50);(3,4)(5,9)(6,13)(7,10)(8,15)(11,16)(12,18)(14,17)(19,21,24,32)(20,25,27,29)(22,30,35,47)(23,31,37,49)(26,38,40,43)(28,39,41,44)(33,50,42,45)(34,46,36,48);(3,5,7,12)(4,9,10,18)(6,14,15,11)(8,16,13,17)(19,22)(20,26)(21,30)(23,36)(24,35)(25,38)(27,40)(28,42)(29,43)(31,48)(32,47)(33,41)(34,37)(39,45)(44,50)(46,49)

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, 94591);