C₁₉×#20580 #18026539

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₉×#20580

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂³×#41×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

3958 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 3958 conjugacy classes of subgroups — too many to draw. Only its 622 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 — 4 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)(22,23)(24,25)(26,27)(28,29,31,35,32,34,38,41)(30,33,37,40,36,39,42,43);(21,23)(28,30)(29,33)(31,37)(32,36)(34,39)(35,40)(38,42)(41,43);(25,27)(30,36)(33,39)(37,42)(40,43);(29,34)(33,39)(35,41)(40,43)

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, 13568);