C₁₉×#1952 #14559809

order	2432
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1952

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

196 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12940, C₁₉×#12941, C₁₉×#12945, …
maximal normal subgroup of	C₁₉×#12940, C₁₉×#12941, C₁₉×#12945, …
maximal quotient of	C₁₉×#9608, C₁₉×#9610, C₁₉×#9613, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 684);