C₁₉×#8492 #18014451

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#8492

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,25,26)(28,29)(30,38,41,34)(31,42,44,51)(32,37)(33,36)(35,43,49,45)(39,54)(40,53,58,48)(46,50)(47,55)(52,57)(56,59);(20,21)(22,26)(23,25)(24,27)(28,30,33,41)(29,34,36,38)(31,39,44,56)(32,40,46,58)(35,47,49,52)(37,48,50,53)(42,59,51,54)(43,55,45,57);(22,27)(24,26)(28,31)(29,35)(30,39)(32,45)(33,44)(34,47)(36,49)(37,51)(38,52)(40,57)(41,56)(42,50)(43,46)(48,54)(53,59)(55,58)

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, 1480);