C₁₉×#2019 #14559876

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2019

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 608

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)(22,23)(24,25,28,32)(26,33,36,38)(27,30,37,31)(29,34,39,35);(21,23)(24,26)(25,29)(27,34)(28,36)(30,33)(31,38)(32,39)(35,37);(25,30)(26,34)(27,37)(31,32)(33,38)(35,36)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2019, C₁₉×#23438, C₁₉×#23439, …
maximal normal subgroup of	C₂×C₁₉×#2019, C₁₉×#23438, C₁₉×#23439, …
maximal quotient of	C₁₉×#9975, C₁₉×#9978, C₁₉×#9987, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 751);