C₁₉×#10099 #18016058

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10088
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10099

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

474 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 102 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)(20,21,25,29)(22,30,23,27)(24,33,34,28)(26,32,35,31)(36,37,40,43)(38,44,45,51)(39,47,48,42)(41,49,50,46);(20,22,25,23)(21,26,29,35)(24,32,34,31)(27,33,30,28)(39,48)(42,47)(44,51)(46,49);(20,23,25,22)(21,27,29,30)(24,31,34,32)(26,28,35,33)(36,38)(37,41)(39,49)(40,45)(42,51)(43,50)(44,47)(46,48)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3087);