C₁₉×#8539 #18014498

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8534
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#8539

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

1008 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 150 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)(20,21)(22,26,27,24)(23,25)(28,29,32,36,33,37,43,49)(30,34,40,46,39,45,53,57)(31,35,42,48,41,47,54,58)(38,50,52,59,51,44,55,56);(20,22)(21,24)(23,27)(25,26)(28,30)(29,34)(31,38)(32,40)(33,39)(35,44)(36,46)(37,45)(41,51)(42,52)(43,53)(47,50)(48,56)(49,57)(54,55)(58,59);(28,31)(29,35)(30,38)(32,42)(33,41)(34,44)(36,48)(37,47)(39,51)(40,52)(43,54)(45,50)(46,56)(49,58)(53,55)(57,59)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1527);