C₁₉×#10383 #18016342

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10383

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

404 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 90 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)(21,26,28,39)(22,30)(23,35)(27,43,44,38)(29,42,40,31)(33,49)(34,47)(36,37)(41,45,48,51)(46,50);(21,27,28,44)(22,30)(23,36)(26,38,39,43)(29,45,40,51)(31,48,42,41)(33,50)(34,47)(35,37)(46,49);(20,21,25,29)(22,31,30,39)(23,27,37,45)(24,28,32,40)(26,34,42,47)(33,43,46,48)(35,51,36,44)(38,50,41,49)

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, 3371);