C₁₉×#1983 #14559840

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1983

Subgroups

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

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

normal subgroups only

This group has 344 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) = 35
transitive degree	μ_t(G) = 1216

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)(21,23)(25,27)(28,29,32,33,31,34,30,35);(20,21,22,23)(29,33)(30,32)(34,35);(24,25,26,27)(29,34)(33,35)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8510, C₁₉×#8511, C₁₉×#10508, …
maximal normal subgroup of	C₁₉×#8510, C₁₉×#8511, C₁₉×#10508, …
maximal quotient of	C₁₉×#9675, C₁₉×#9676, C₁₉×#9697, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 715);