C₁₉×#8534 #18014493

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8534
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#8534

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₁₉×#3484	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25,27,32)(22,28)(26,31,33,35)(29,34);(20,21)(22,25)(23,27)(24,26)(28,32)(29,31)(30,33)(34,35);(22,29)(25,31)(28,34)(32,35)

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, 1522);