C₁₉×#20329 #18026288

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³×C₁₉ · Schur multiplier (H₂) = C₂²×C₄³

Aliases

direct product

C₁₉×#20329

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂	C₂×C₄³×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

1502 conjugacy classes of subgroups; only the 1294 normal subgroups are shown.

normal subgroups only

This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 1294 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) = 2432

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

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 13317);