C₁₉×#13722 #18019681

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#13722

Subgroups

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

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

normal subgroups only

This group has 184 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) = 2432

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6710);