C₁₉×#11916 #18017875

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11916

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1533
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#97	C₂³×C₁₉
prime radical	C₂³×C₁₉	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 274 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)(20,21,23,29,24,30,37,48,25,27,36,44,39,28,45,46)(22,31,32,49,33,26,40,42,34,43,50,47,38,41,35,51);(20,22,25,34)(21,26,27,41)(23,35,36,40)(24,38,39,33)(28,43,30,31)(29,47,44,49)(32,37,50,45)(42,46,51,48);(21,27)(23,36)(26,41)(28,30)(31,43)(32,50)(35,40)(37,45)

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, 4904);