C₁₉×#1385 #14559242

order	2432
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1385

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#106
commutator	C₈	C₄²×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7424, C₁₉×#7425, C₂×C₁₉×#1385, …
maximal normal subgroup of	C₁₉×#7424, C₁₉×#7425, C₂×C₁₉×#1385, …
maximal quotient of	C₁₉×#7157, C₁₉×#7173, C₁₉×#7220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 117);

C19×#1385 #14559242

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1385 #14559242