C₁₉×#1384 #14559241

order	2432
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1384

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	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

132 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)(22,32,34,46)(23,29)(24,39)(25,41)(26,31)(27,33,42,47)(28,37)(30,40)(35,50,48,44)(36,51,49,43)(38,45);(20,22,24,35,40,49,38,47,26,34,37,48,25,36,23,33)(21,27,29,43,41,50,28,32,31,42,45,51,30,44,39,46)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7422, C₁₉×#7423, C₂×C₁₉×#1384, …
maximal normal subgroup of	C₁₉×#7422, C₁₉×#7423, C₂×C₁₉×#1384, …
maximal quotient of	C₁₉×#7157, C₁₉×#7174, C₁₉×#7218, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 116);

C19×#1384 #14559241

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1384 #14559241