C₁₉×#1439 #14559296

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#1439

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂³
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7250, C₁₉×#8403, C₁₉×#8405, …
maximal normal subgroup of	C₁₉×#7250, C₁₉×#8403, C₁₉×#8405, …
maximal quotient of	C₁₉×#7555, C₁₉×#7556, C₁₉×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 171);

C19×#1439 #14559296

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1439 #14559296