C₁₉×#2050 #14559907

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2050

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#394
prime radical	C₁₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7414, C₁₉×#7415, C₁₉×#12173, …
maximal normal subgroup of	C₁₉×#7414, C₁₉×#7415, C₁₉×#12173, …
maximal quotient of	C₁₉×#10456, C₁₉×#10457, C₁₉×#10458, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 782);