C₁₉×#11486 #18017445

order	4864
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#11486

Subgroups

	subgroup	G/H
center	C₄×C₁₉	C₂×#99
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#1459
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

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

normal subgroups only

This group has 364 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) = 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)(20,21,25,31,27,32,39,51,26,33,43,44,24,30,35,50)(22,34,37,47,36,46,23,29,38,48,41,49,42,28,40,45);(20,22)(21,28)(23,39)(24,42)(25,37)(26,38)(27,36)(29,31)(30,48)(32,34)(33,46)(35,40)(41,43)(44,45)(47,50)(49,51);(20,23,27,41,26,40,24,37)(21,29,32,49,33,45,30,47)(22,35,36,25,38,39,42,43)(28,44,34,50,46,31,48,51)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4474);