C₁₉×#12591 #18018550

order	4864
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#12591

Subgroups

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

390 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 254 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) = 47
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,29)(27,28)(30,31)(32,33,34,38,35,39,40,45,36,37,41,43,42,44,46,47);(20,21,22,23)(25,28)(29,31);(24,26,27,30)(25,29,28,31)(33,37)(38,43)(39,44)(45,47)

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5579);