C₁₉×#10226 #18016185

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10226

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

488 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 114 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)(21,24)(22,26)(25,27)(28,29,34,39)(30,40,43,51)(31,36,47,54)(32,38,33,37)(35,44,50,42)(41,56,57,52)(45,59,58,49)(46,55,48,53);(20,21,23,25)(22,27,26,24)(28,30,34,43)(29,35,39,50)(31,45,47,58)(32,44,33,42)(36,52,54,56)(37,51,38,40)(41,48,57,46)(49,55,59,53);(20,21)(22,27)(23,25)(24,26)(28,31)(29,36)(30,41)(32,46)(33,48)(34,47)(35,49)(37,53)(38,55)(39,54)(40,52)(42,45)(43,57)(44,58)(50,59)(51,56)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3214);