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C₂²⋊D₄₉ #87627

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 53 points:

(1,28,35,22,42,40,9,7,37,24,11,48,31,4,16,26,12,38,47,19,13,29,14,5,46,41,10,25,17,6,27,49,32,23,36,8,2,39,43,20,34,30,3,15,45,33,21,44,18)(51,53);(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,22)(24,34)(26,36)(30,37)(31,39)(32,38)(33,42)(35,44)(40,45)(41,46)(43,48)(47,49)(50,51)(52,53)

Polycyclic presentation:

2^3,7^2|d^7=e^6,b^a=bc,d^a=d^6e,e^a=e^6

Conjugacy classes & character table

101 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 7);