C₁₉×#9444 #18015403

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9443
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#9444

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

474 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 51
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25,29,32)(23,26)(24,27)(28,31,34,35)(30,33)(36,37)(38,45,46,49)(39,42,47,48)(40,43)(41,44)(50,51);(20,22)(21,25,27,32)(23,28)(24,29)(26,31,33,35)(30,34)(36,38,40,48,41,46,50,42)(37,39,43,49,44,47,51,45);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,31,32,35)(36,39)(37,42)(38,43)(40,49)(41,47)(44,48)(45,50)(46,51)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 2432);