C₁₉×#8529 #18014488

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8528
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#8529

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3553	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 648 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)(21,26)(22,29)(23,24)(28,31)(30,32)(33,34)(36,37)(38,46,49,42)(39,50,51,61)(40,45)(41,44)(43,52,58,54)(47,63)(48,60,53,57)(55,59)(56,65)(62,66)(64,67);(20,21,25,28)(22,27,30,35)(23,31,24,26)(29,34,32,33)(36,38,41,49)(37,42,44,46)(39,47,51,64)(40,53,55,48)(43,56,58,62)(45,60,59,57)(50,63,61,67)(52,66,54,65);(20,22)(21,27)(23,29)(24,32)(25,30)(26,33)(28,35)(31,34)(36,39)(37,43)(38,47)(40,54)(41,51)(42,56)(44,58)(45,61)(46,62)(48,66)(49,64)(50,59)(52,55)(53,65)(57,63)(60,67)

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, 1517);