C₁₉×#7363 #18013322

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7363

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
socle	C₂²×C₁₉	C₂²⋊C₁₆
prime radical	C₂³×C₁₉	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 91
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,27,24)(23,25)(28,29,32,38,33,39,51,64,34,40,52,65,54,67,79,87,35,41,53,66,55,68,80,88,31,37,48,61,49,62,76,85)(30,42,44,69,45,70,73,89,43,59,71,63,72,83,90,86,46,60,50,77,74,84,78,91,47,36,56,57,75,58,81,82);(20,22,23,27)(21,24,25,26)(28,30)(29,36)(31,47)(32,50)(33,45)(34,43)(35,46)(37,60)(38,63)(39,58)(40,42)(41,59)(44,53)(48,71)(49,75)(51,78)(52,56)(54,72)(55,74)(57,66)(61,69)(62,84)(64,86)(65,77)(67,70)(68,83)(73,80)(76,90)(79,81)(82,88)(85,89)(87,91)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 351);