C₁₉×#7156 #18013115

order	4864
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7156

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#106
commutator	C₈	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

234 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 142 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 — 2 generators on 47 points:

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

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 144);