C₁₉×#8796 #18014755

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

Aliases

direct product

C₁₉×#8796

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 228 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)(20,21,24,30,26,31,25,29)(22,28,23,27,33,34,32,35)(36,37,41,47,42,45,40,46)(38,48,50,60,51,43,55,58)(39,52,53,59,54,61,56,44)(49,63,65,62,66,67,64,57);(20,22,25,32,26,33,24,23)(21,27,30,34,31,35,29,28)(36,38,40,50,42,51,41,55)(37,43,46,58,45,48,47,60)(39,49,53,64,54,66,56,65)(44,57,52,67,59,62,61,63);(20,23,24,33,26,32,25,22)(21,28,29,35,31,34,30,27)(36,39)(37,44,45,59)(38,49)(40,53)(41,56)(42,54)(43,57,48,62)(46,52,47,61)(50,64)(51,66)(55,65)(58,67,60,63)

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, 1784);