C₁₉×#11311 #18017270

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#11311

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#396
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#1443
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

532 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 202 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)(22,32)(23,36,40,28)(24,30)(25,31)(26,29)(27,34)(33,44,48,49)(35,47)(37,42,50,51)(38,45,39,46)(41,43);(20,22,26,34,25,35,24,41)(21,27,29,47,31,43,30,32)(23,37,38,33,40,50,39,48)(28,44,46,51,36,49,45,42);(20,23,24,38,25,40,26,39)(21,28,29,45,31,36,30,46)(22,33,34,37,35,48,41,50)(27,42,32,44,43,51,47,49)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4299);