C₁₉×#11990 #18017949

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11990

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1551
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

268 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,25,29,43,55,26,32,44,58,46,31,59,57)(22,33,35,61,36,50,65,75,37,49,66,56,45,27,42,48)(23,38,40,67,41,28,51,52,39,54,68,80,69,53,77,79)(34,47,63,73,64,60,81,82,62,74,76,83,71,72,70,78);(20,22,26,37)(21,27,32,50)(23,34,39,62)(24,42,44,65)(25,45,46,36)(28,47,53,74)(29,49,31,33)(30,56,58,61)(35,43,66,59)(38,60,54,72)(40,70,68,81)(41,71,69,64)(48,55,75,57)(51,76,77,63)(52,78,79,82)(67,73,80,83);(20,23)(21,28,32,53)(22,34)(24,40)(25,41)(26,39)(27,47,50,74)(29,54,31,38)(30,52,58,79)(33,60,49,72)(35,63)(36,64)(37,62)(42,70)(43,51)(44,68)(45,71)(46,69)(48,73,75,83)(55,80,57,67)(56,78,61,82)(59,77)(65,81)(66,76)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4978);