C₁₉×#1991 #14559848

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1991

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

252 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 47
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7135, C₁₉×#7359, C₁₉×#8529, …
maximal normal subgroup of	C₁₉×#7135, C₁₉×#7359, C₁₉×#8529, …
maximal quotient of	C₁₉×#9871, C₁₉×#9875, C₁₉×#9886, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 723);