C₁₉×#7516 #18013475

order	4864
nilpotency class	6
isoclinism	isoclinic class of #7515
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7516

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1402
commutator	#127	C₂×C₄×C₁₉
Frattini, cosocle	#493	C₂²×C₁₉
prime radical	C₁₉×#493	C₂²
LCS	G ▷ #127 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#493 ◁ G

162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 generators on 35 points:

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

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 504);