C₁₉×#1745 #14559602

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1745

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂²	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#7023, C₁₉×#7043, C₁₉×#7048, …
maximal normal subgroup of	C₁₉×#7023, C₁₉×#7043, C₁₉×#7048, …
maximal quotient of	C₁₉×#8132, C₁₉×#8134, C₁₉×#8136, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 477);

C19×#1745 #14559602