C₁₉×#10393 #18016352

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10393

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,21,24,28)(22,26,33,42)(23,34)(25,30,38,29)(27,36)(31,46)(32,41,48,40)(35,43)(37,44)(39,49)(45,50)(47,51);(20,22)(21,26)(23,35,36,31)(24,33)(25,32)(27,43,34,46)(28,42)(29,40)(30,41)(37,49,50,47)(38,48)(39,44,51,45);(20,23,25,37)(21,27,30,45)(22,31,32,47)(24,36,38,50)(26,39,41,43)(28,34,29,44)(33,35,48,49)(40,46,42,51)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3381);