C₁₉×#1765 #14559622

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1765

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,28,32,29,33,27,30)(26,31,36,38,34,39,35,37);(21,23)(25,30,33,32)(26,34)(31,38,39,37)(35,36);(24,26,28,36,29,34,27,35)(25,31,32,38,33,39,30,37)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12618, C₁₉×#13127, C₂×C₁₉×#1765, …
maximal normal subgroup of	C₁₉×#12618, C₁₉×#13127, C₂×C₁₉×#1765, …
maximal quotient of	C₁₉×#8185, C₁₉×#8186, C₁₉×#8188, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 497);

C19×#1765 #14559622

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1765 #14559622