C₁₉×#1905 #14559762

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1902
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1905

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#386
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 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)(20,21,25,29,26,31,24,30)(22,32,35,42,36,45,34,27)(23,37,39,28,40,43,38,44)(33,41,48,50,49,51,47,46);(20,22)(21,27,31,42)(23,33)(24,34)(25,35)(26,36)(28,41,44,51)(29,32,30,45)(37,46,43,50)(38,47)(39,48)(40,49);(20,23,26,40)(21,28,31,44)(22,33,36,49)(24,39,25,38)(27,41,42,51)(29,37,30,43)(32,46,45,50)(34,48,35,47)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1905, C₁₉×#20998, C₁₉×#22284, …
maximal normal subgroup of	C₂×C₁₉×#1905, C₁₉×#20998, C₁₉×#22284, …
maximal quotient of	C₁₉×#9088, C₁₉×#9090, C₁₉×#9092, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 637);