C₁₉×#9429 #18015388

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

Aliases

direct product

C₁₉×#9429

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

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

normal subgroups only

This group has 508 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) = 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)(20,21,25,27,24,22,23,26)(28,29,33,37,34,39,32,38)(30,40,43,50,44,53,42,35)(31,45,47,36,48,51,46,52)(41,49,56,58,57,59,55,54);(20,22,24,21)(23,26,25,27)(28,30)(29,35,39,50)(31,41)(32,42)(33,43)(34,44)(36,49,52,59)(37,40,38,53)(45,54,51,58)(46,55)(47,56)(48,57);(23,25)(26,27)(28,31,34,48)(29,36,39,52)(30,41,44,57)(32,47,33,46)(35,49,50,59)(37,45,38,51)(40,54,53,58)(42,56,43,55)

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, 2417);