C₁₉×#9421 #18015380

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9421

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
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

488 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 2432

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)(20,21,25,27,24,22,23,26)(28,29)(30,39)(31,43,46,53)(32,47)(33,37)(34,38)(35,41)(36,45,52,44)(40,55,57,49)(42,50)(48,51)(54,56,59,58);(20,22,24,21)(23,26,25,27)(28,30,32,41,34,42,33,48)(29,35,37,39,38,51,47,50)(31,40,45,58,46,57,44,56)(36,49,53,54,52,55,43,59);(23,25)(26,27)(28,31)(29,36)(30,40)(32,45)(33,44)(34,46)(35,49)(37,53)(38,52)(39,54)(41,58)(42,57)(43,47)(48,56)(50,59)(51,55)

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, 2409);