C₁₉×#8317 #18014276

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#8317

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#3459	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

864 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1305);