C₁₉×#13373 #18019332

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13373

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#2023
prime radical	C₂×C₁₉×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

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

normal subgroups only

This group has 364 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) = 608

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

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, 6361);