C₁₉×#8794 #18014753

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×#8794

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)(20,21,25,22)(23,24,27,26)(28,29)(30,38,41,34)(31,42,45,57)(32,37)(33,36)(35,44,50,54)(39,53)(40,52,56,48)(43,58)(46,51)(47,55)(49,59);(20,22,24,27,25,21,26,23)(28,30,32,40,33,41,46,56)(29,34,37,48,36,38,51,52)(31,43,44,59,45,39,54,55)(35,49,42,53,50,47,57,58);(20,23,24,22,25,27,26,21)(28,31)(29,35,36,50)(30,39)(32,44)(33,45)(34,47,38,49)(37,42,51,57)(40,55)(41,43)(46,54)(48,58,52,53)(56,59)

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, 1782);