C₁₉×#12062 #18018021

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12062

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₈×D₄
prime radical	C₂×D₈×C₁₉	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

252 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 130 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 — 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)(22,24,27,26)(28,29,31,35,32,36,39,42,33,30,34,37,40,38,41,43);(21,24)(22,27)(25,26);(21,25)(24,26)(28,30,31,37,32,38,39,43,33,29,34,35,40,36,41,42)

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5050);