C₁₉×#8799 #18014758

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#8799

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

220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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)(20,21,25,29,26,31,24,30)(22,28,32,35,33,34,23,27)(36,37,40,45,41,44,47,57)(38,46,50,59,51,42,49,60)(39,52,55,43,56,63,54,62)(48,64,65,58,53,67,66,61);(20,22,24,23,26,33,25,32)(21,27,29,28,31,35,30,34)(36,38,47,50,41,51,40,49)(37,42,57,60,44,46,45,59)(39,53,55,65,56,48,54,66)(43,61,63,67,62,58,52,64);(20,23,24,33,26,32,25,22)(21,28,29,35,31,34,30,27)(36,39)(37,43,44,62)(38,48)(40,54)(41,56)(42,58,46,61)(45,52,57,63)(47,55)(49,65)(50,66)(51,53)(59,67,60,64)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1787);