C₁₉×#1876 #14559733

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1876

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

324 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)(21,23)(25,29,31,34)(26,32,33,35);(20,21,22,23)(24,25,27,34,28,31,36,29)(26,30,35,38,33,39,32,37);(24,26)(25,30)(27,35)(28,33)(29,37)(31,39)(32,36)(34,38)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1876, C₁₉×#20917, C₁₉×#20918, …
maximal normal subgroup of	C₂×C₁₉×#1876, C₁₉×#20917, C₁₉×#20918, …
maximal quotient of	C₁₉×#8945, C₁₉×#8946, C₁₉×#8947, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 608);

C19×#1876 #14559733

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1876 #14559733