C₁₉×#8495 #18014454

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#8495

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 620 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) = 1216

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)(21,25,27,30)(26,34,35,33)(36,37)(38,46,49,42)(39,50,52,59)(40,45)(41,44)(43,51,57,53)(47,62)(48,61,66,56)(54,58)(55,63)(60,65)(64,67);(20,21)(22,26)(23,30)(24,27)(25,32)(28,33)(29,35)(31,34)(36,38,41,49)(37,42,44,46)(39,47,52,64)(40,48,54,66)(43,55,57,60)(45,56,58,61)(50,67,59,62)(51,63,53,65);(20,22,24,29)(21,26,27,35)(23,31,32,28)(25,33,30,34)(36,39)(37,43)(38,47)(40,53)(41,52)(42,55)(44,57)(45,59)(46,60)(48,65)(49,64)(50,58)(51,54)(56,62)(61,67)(63,66)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1483);