C₁₉×#12513 #18018472

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12506
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#12513

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#1712	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

290 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 94 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)(22,28)(23,31)(24,26)(25,29)(27,32)(30,34)(33,35)(37,44)(38,48)(39,40)(41,42)(45,47)(46,50)(49,51);(20,22,23,29,24,30,32,35)(21,25,27,28,26,33,31,34)(36,37,40,45,41,46,49,38,43,48,51,50,42,47,39,44);(21,26)(25,33)(27,31)(28,34)(36,38,49,47,42,45,40,48,43,44,39,46,41,50,51,37)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5501);