C₁₉×#6887 #17987273

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₁₉ · Schur multiplier (H₂) = C₃×C₉

Aliases

direct product

C₁₉×#6887

Subgroups

	subgroup	G/H
center	C₃×C₉×C₁₉	C₃²
commutator	C₃	C₃²×C₉×C₁₉
Frattini, cosocle	C₃²	C₃³×C₁₉
socle	C₃²×C₁₉	C₃³
prime radical	C₃³×C₁₉	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₉ ◁ G

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22,24,26,25,27,28)(29,30,33)(31,35,41)(32,36,40)(34,42,39)(37,44,49)(38,45,48)(43,50,47)(46,52,54)(51,55,53);(30,34,36)(33,40,42)(35,43,45)(41,48,50)(44,51,52)(49,54,55);(29,31,37,32,38,46,39,47,53)(30,35,44,36,45,52,34,43,51)(33,41,49,40,48,54,42,50,55)

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28353184, #28353186, #28353190, …
maximal subgroup of	C₁₉×#10624457, C₁₉×#10624458, C₁₉×#10624460, …
maximal normal subgroup of	C₁₉×#10624457, C₁₉×#10624458, C₁₉×#10624460, …
maximal quotient of	C₁₉×#10624544, C₉×C₁₉×C₃²⋊C₉, C₉×C₁₉×C₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 34);

C19×#6887 #17987273