C₁₉×#1851 #14559708

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1851

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

324 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 136 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)(20,21)(22,23)(24,25)(26,27)(28,29,32,30,31,33,35,34);(21,23)(28,30,32,33,31,34,35,29);(25,27)(29,33)(30,34)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7067, C₁₉×#8874, C₁₉×#8875, …
maximal normal subgroup of	C₁₉×#7067, C₁₉×#8874, C₁₉×#8875, …
maximal quotient of	C₁₉×#8832, C₁₉×#8833, C₁₉×#8834, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 583);