C₁₉×#2110 #14559967

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2110

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₄²
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₂×#97
prime radical	C₂³×C₁₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ G

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#11912, C₁₉×#11913, C₁₉×#11914, …
maximal normal subgroup of	C₁₉×#11912, C₁₉×#11913, C₁₉×#11914, …
maximal quotient of	C₁₉×#11405, C₁₉×#11406, C₁₉×#11413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 842);

C19×#2110 #14559967

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2110 #14559967