C₁₉×#1839 #14559696

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1839

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7019, C₁₉×#7023, C₁₉×#7041, …
maximal normal subgroup of	C₁₉×#7019, C₁₉×#7023, C₁₉×#7041, …
maximal quotient of	C₁₉×#8800, C₁₉×#8801, C₁₉×#10795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 571);

C19×#1839 #14559696