C₁₉×#8142 #18014101

order	4864
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#8142

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

294 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 158 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)(20,21,24,27,23,26,31,34)(22,28,30,35,29,25,32,33)(36,37)(38,46,49,59)(39,43)(40,44)(41,45)(42,48,54,62)(47,58,61,66)(50,55)(51,56)(52,57)(53,60,64,67)(63,65);(20,22)(21,25)(23,29)(24,30)(26,28)(27,33)(31,32)(34,35)(36,38)(37,42,45,54)(39,47)(40,48)(41,49)(43,53,56,64)(44,46,57,59)(50,60)(51,61)(52,62)(55,58,65,66)(63,67);(22,29)(25,28)(30,32)(33,35)(36,39,40,50,41,51,52,63)(37,43,44,55,45,56,57,65)(38,47,48,60,49,61,62,67)(42,53,46,58,54,64,59,66)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1130);