C₁₉×#10216 #18016175

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10216

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

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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)(22,24)(23,26)(25,27)(28,29,34,39)(30,40,43,54)(31,44,47,52)(32,38,33,37)(35,48,50,42)(36,45,53,46)(41,49,57,51)(55,58,59,56);(21,24)(22,27)(25,26)(28,30)(29,35)(31,41)(32,48)(33,42)(34,43)(36,51)(37,54)(38,40)(39,50)(44,55)(45,58)(46,56)(47,57)(49,53)(52,59);(20,21,23,26)(22,25,27,24)(28,31,34,47)(29,36,39,53)(30,41,43,57)(32,46,33,45)(35,49,50,51)(37,44,38,52)(40,55,54,59)(42,58,48,56)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3204);