C₁₉×#1436 #14559293

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#1436

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂³
commutator	C₂²	C₂×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

612 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2432

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)(21,23)(24,25,27,26)(29,31)(32,33,35,34);(28,29)(30,31)(32,33,35,34);(20,21)(22,23)(24,26,27,25)(28,29)(30,31)(32,34,35,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#7215, C₁₉×#8347, C₂×C₁₉×#1436, …
maximal normal subgroup of	C₁₉×#7215, C₁₉×#8347, C₂×C₁₉×#1436, …
maximal quotient of	C₁₉×#7554, C₁₉×#7556, C₁₉×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 168);

C19×#1436 #14559293