C₁₉×#10612 #18016571

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10612

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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)(20,21,23,29,25,27,24,28)(22,30,31,26,33,34,32,35)(36,37,40,44)(38,45,47,50)(39,42,46,43)(41,49,51,48);(20,22,24,32,25,33,23,31)(21,26,29,34,27,35,28,30)(36,38,46,49,40,47,39,48)(37,41,42,50,44,51,43,45);(21,27)(22,31)(23,24)(26,34)(30,35)(32,33)(37,42)(38,47)(39,46)(41,50)(43,44)(45,51)

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, 3600);