C₁₉×#8476 #18014435

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#8476

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3512	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

678 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27,24,25,31,33)(22,28,29,35,30,26,32,34)(36,37)(38,46)(39,50,52,43)(40,53)(41,45)(42,48)(44,56)(47,62,64,67)(49,60)(51,59,55,61)(54,58)(57,63,66,65);(21,25)(23,31)(26,28)(29,32)(36,38)(37,42)(39,47)(40,54)(41,49)(43,57)(44,60)(45,58)(46,53)(48,56)(50,66)(51,65)(52,64)(55,63)(59,62)(61,67);(20,22,24,30)(21,26,25,28)(23,32,31,29)(27,35,33,34)(36,39,41,52)(37,43,45,50)(38,47,49,64)(40,55,56,51)(42,57,58,66)(44,61,53,59)(46,62,60,67)(48,65,54,63)

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, 1464);