C₁₉×#8792 #18014751

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₉×#8792

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

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, 1780);