C₁₉×#12851 #18018810

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12851

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#381
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1817
prime radical	C₂⁴×C₁₉	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

416 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5839);