C₁₉×#7466 #18013425

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7466

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₄²
commutator	C₄	C₄×C₁₆×C₁₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
socle	C₂²×C₁₉	#346
prime radical	C₂³×C₁₉	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

182 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,27,33,28,35,39,48,29,31,40,43,41,44,52,53,30,34,38,47,42,49,51,55,26,32,36,45,37,46,50,54);(21,23)(25,31,34,32)(27,38)(33,45,47,43)(35,44,49,46)(36,40)(39,51)(48,54,55,53)(50,52)

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, 454);