C₁₉×#8744 #18014703

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8738
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#8744

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

384 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 51
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29,31,25)(23,28)(24,27)(26,30,33,35)(32,34)(36,37,39,43,40,42,46,49)(38,41,44,48,45,47,50,51);(20,22)(21,25)(23,30)(24,31)(26,28)(27,29)(32,35)(33,34)(36,38,40,45)(37,41,42,47)(39,44,46,50)(43,48,49,51);(20,22)(21,26,27,33)(23,30)(24,31)(25,28,29,34)(32,35)(37,42)(39,46)(41,47)(44,50)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1732);