C₁₉×#13728 #18019687

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#13728

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₂×C₁₉×D₃₂	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

238 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 87
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,36)(27,42)(28,32)(29,48)(30,49)(31,38)(33,37)(34,43)(35,47)(39,56)(40,69)(41,70)(44,71)(45,75)(46,76)(50,65)(51,79)(52,80)(53,61)(54,74)(55,81)(57,60)(58,64)(59,68)(62,73)(63,72)(66,77)(67,86)(78,87)(82,84)(83,85);(24,26,37,60,29,40,62,80,47,68,81,87,74,85,44,65,28,39,61,84,46,67,45,66,30,41,63,79,43,64,27,38)(25,31,42,58,34,51,72,70,49,77,75,86,76,82,53,56,32,50,71,83,54,78,55,59,35,52,73,69,48,57,33,36);(20,21,22,23)(25,32)(31,50)(33,53)(34,54)(35,49)(36,56)(42,71)(48,76)(51,78)(52,77)(55,72)(57,82)(58,83)(59,70)(69,86)(73,75)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6716);