C₁₉×#9422 #18015381

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×#9422

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#123
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 384 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,29,25,22,24,28)(23,27,33,35,32,30,31,34)(36,37)(38,47)(39,51,54,61)(40,55)(41,45)(42,46)(43,49)(44,53,60,52)(48,63,65,57)(50,58)(56,59)(62,64,67,66);(20,22,25,21)(23,30,32,27)(24,28,26,29)(31,34,33,35)(36,38,40,49,42,50,41,56)(37,43,45,47,46,59,55,58)(39,48,53,66,54,65,52,64)(44,57,61,62,60,63,51,67);(20,23,25,32)(21,27,22,30)(24,33,26,31)(28,35,29,34)(36,39)(37,44)(38,48)(40,53)(41,52)(42,54)(43,57)(45,61)(46,60)(47,62)(49,66)(50,65)(51,55)(56,64)(58,67)(59,63)

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, 2410);