C₁₉×#2026 #14559883

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2026

Subgroups

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

258 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 100 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)(24,25,27,29)(26,30,31,28)(32,33,35,37)(34,40,41,47)(36,44,43,39)(38,45,46,42);(20,21)(22,23)(24,26,27,31)(25,28,29,30)(33,37)(38,46)(39,44)(40,47);(21,23)(32,34,35,41)(33,38,37,46)(36,45,43,42)(39,47,44,40)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7429, C₂×C₁₉×#2026, C₁₉×#23451, …
maximal normal subgroup of	C₁₉×#7429, C₂×C₁₉×#2026, C₁₉×#23451, …
maximal quotient of	C₁₉×#10345, C₁₉×#10347, C₁₉×#10352, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 758);