C₁₉×#8798 #18014757

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×#8798

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

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, 1786);