C₁₉×#13706 #18019665

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13706

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 4864

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

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6694);