C₁₉×#7387 #18013346

order	4864
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7387

Subgroups

	subgroup	G/H
center	C₈×C₁₉	D₁₆
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	#1331
prime radical	C₁₉×#508	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 83 points:

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

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, 375);