C₁₉×#10666 #18016625

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10666

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#399
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 354 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)(20,21,25,26,24,22,23,27)(28,29,34,38,33,39,32,37)(30,40,48,35,43,51,42,50)(31,36,46,55,47,54,45,53)(41,56,44,59,58,52,57,49);(20,22,24,21)(23,27,25,26)(28,30,32,48,33,43,34,42)(29,35,37,51,39,50,38,40)(31,44,45,58,47,57,46,41)(36,52,53,49,54,56,55,59);(21,26)(22,27)(23,25)(28,31)(29,36)(30,41)(32,45)(33,47)(34,46)(35,49)(37,53)(38,55)(39,54)(40,52)(42,57)(43,58)(44,48)(50,59)(51,56)

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, 3654);