C₁₉×#8791 #18014750

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#8791

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 1216

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)(22,30)(23,26)(24,34)(25,29)(27,32)(28,31)(33,35)(36,37)(38,46,50,42)(39,51,53,66)(40,45)(41,44)(43,52,57,61)(47,54)(48,62)(49,59,60,56)(55,63)(58,67)(64,65);(20,22,31,33,25,32,24,23)(21,26,34,27,29,35,28,30)(36,38,47,60,41,50,40,49)(37,42,54,59,44,46,45,56)(39,48,61,67,53,64,52,63)(43,55,66,62,57,58,51,65);(20,23,24,32,25,33,31,22)(21,27,28,26,29,30,34,35)(36,39)(37,43,44,57)(38,48)(40,52)(41,53)(42,55,46,58)(45,51,54,66)(47,61)(49,63)(50,64)(56,65,59,62)(60,67)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1779);