C₁₉×#2966 #14560823

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2966

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₁₉×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 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)(22,25)(23,24)(26,27)(28,29,31,35,32,34,38,41)(30,33,36,40,37,39,42,43);(21,24)(25,27);(28,30,31,36,32,37,38,42)(29,33,35,40,34,39,41,43);(20,22,23,26)(21,25,24,27)(29,34)(33,39)(35,41)(40,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#8247, C₁₉×#8248, C₁₉×#8249, …
maximal normal subgroup of	C₁₉×#8247, C₁₉×#8248, C₁₉×#8249, …
maximal quotient of	C₁₉×#20474, C₁₉×#20476, C₁₉×#20484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1698);

C19×#2966 #14560823