C₁₉×#8636 #18014595

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8626
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#8636

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#380
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

404 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,25,23,24,26,27)(28,29,33,36,34,31,32,42)(30,37,40,38,41,43,39,35);(28,30,32,39,34,41,33,40)(29,35,36,37,31,38,42,43);(21,24)(22,26)(28,31)(29,34)(30,38)(32,42)(33,36)(35,41)(37,40)(39,43)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1624);