C₁₉×#7160 #18013119

order	4864
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7160

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	D₈
commutator	C₈	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#335
prime radical	C₂³×C₁₉	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 210 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) = 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)(24,25,27,34,30,35,43,49,31,36,44,50,29,45,28,33)(26,37,38,32,41,46,53,47,42,52,54,48,40,55,39,51);(21,23)(24,26,28,39,29,40,44,54,31,42,43,53,30,41,27,38)(25,32,34,46,35,47,49,52,36,48,50,55,45,51,33,37)

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, 148);