C₁₉×#8632 #18014591

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×#8632

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

388 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 59
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 59 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)(30,39)(31,44,46,51)(32,47)(33,37)(34,38)(35,41)(36,45,52,48)(40,49,56,59)(42,50)(43,54)(53,55,58,57);(28,30,33,42,34,43,32,41)(29,35,47,54,38,50,37,39)(31,40,48,57,46,56,45,55)(36,49,44,58,52,59,51,53);(21,24)(22,26)(28,31)(29,36)(30,40)(32,45)(33,48)(34,46)(35,49)(37,51)(38,52)(39,53)(41,55)(42,57)(43,56)(44,47)(50,59)(54,58)

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, 1620);