C₁₉×#12313 #18018272

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12310
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12313

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3293	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

356 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 608

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)(20,21,26,22)(23,33,36,49)(24,38,43,39)(25,32,41,29)(27,44,30,35)(28,47,31,42)(34,48,37,50)(40,45,51,46);(20,22,26,21)(23,30,36,27)(24,39,43,38)(25,29,41,32)(28,42,31,47)(33,40,49,51)(34,45,37,46)(35,50,44,48);(20,23)(21,27)(22,30)(24,40)(25,34)(26,36)(28,48)(29,45)(31,50)(32,46)(33,38)(35,42)(37,41)(39,49)(43,51)(44,47)

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, 5301);