C₁₉×#8795 #18014754

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#8795

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 270 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,27)(23,24)(28,29)(30,38,42,34)(31,43,46,57)(32,37)(33,36)(35,45,51,54)(39,47)(40,55)(41,52,53,49)(44,58)(48,56)(50,59);(20,21,23,26,25,27,24,22)(28,30,39,53,33,42,32,41)(29,34,47,52,36,38,37,49)(31,44,54,56,46,40,45,59)(35,50,57,58,51,48,43,55);(20,22,23,21,25,26,24,27)(28,31)(29,35,36,51)(30,40)(32,45)(33,46)(34,48,38,50)(37,43,47,57)(39,54)(41,56)(42,44)(49,58,52,55)(53,59)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1783);