C₁₉×#10110 #18016069

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10110

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3253	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

498 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 2432

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)(23,34)(24,27)(25,28)(26,31)(30,33)(32,35)(38,44)(39,46)(41,49)(42,47)(45,48)(50,51);(20,22,25,33)(21,26,28,35)(23,32,24,31)(27,30,34,29)(36,37,40,43)(38,41,45,50)(39,47,46,42)(44,51,48,49);(20,21)(22,30)(23,27)(24,34)(25,28)(26,31)(29,33)(32,35)(36,38)(37,41)(39,48)(40,45)(42,51)(43,50)(44,46)(47,49)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3098);