C₁₉×#8801 #18014760

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#8801

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#383
prime radical	C₂³×C₁₉	#117
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

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

normal subgroups only

This group has 306 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) = 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)(20,21,23,25,22,24,26,27)(28,29)(30,38,41,42)(31,34)(32,36)(33,37)(35,40,43,39);(29,34,37,36)(35,42,43,38);(21,24)(25,27)(28,30,31,39,33,41,32,40)(29,35,36,38,37,43,34,42)

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, 1789);