C₁₉×#7145 #18013104

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#7145

Subgroups

	subgroup	G/H
center	C₄²×C₁₉	C₄²
commutator	C₄	C₄×C₁₆×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ G

222 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 51
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29,31,35)(23,27)(24,33)(25,28)(26,30,34,32)(36,37,38,41,39,42,44,47,40,43,45,48,46,49,50,51);(20,22,24,32,25,31,23,30)(21,26,27,29,28,34,33,35)

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, 133);