C₁₉×#2053 #14559910

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2053

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#394
prime radical	C₁₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

264 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12170, C₁₉×#12171, C₁₉×#12172, …
maximal normal subgroup of	C₁₉×#12170, C₁₉×#12171, C₁₉×#12172, …
maximal quotient of	C₁₉×#10464, C₁₉×#10465, C₁₉×#10466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 785);