C₁₉×#10306 #18016265

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#10306

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

670 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 170 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) = 47
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3294);