C₁₉×#7382 #18013341

order	4864
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7382

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#102
commutator	C₈	C₂×C₁₆×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	D₄⋊C₁₆
prime radical	C₁₉×#135	C₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 118 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) = 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)(20,21,24,31,26,30,47,58,27,32,48,61,23,40,42,70,28,33,49,62,43,59,73,82,25,50,46,77,44,63,74,83)(22,34,36,64,38,29,52,53,37,55,69,79,41,56,71,80,39,66,45,75,35,57,67,60,51,65,76,81,68,54,72,78);(20,22)(21,29)(23,41)(24,45)(25,51)(26,38)(27,37)(28,39)(30,55)(31,60)(32,56)(33,57)(34,63)(35,43)(36,49)(40,66)(42,72)(44,68)(46,69)(47,67)(48,76)(50,54)(52,73)(53,62)(58,81)(59,65)(61,78)(64,70)(71,74)(75,83)(77,80)(79,82)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 370);