Finite Group Databasebeta

← Prev (#14559700) Next (#14559702) →

C₁₉×#1844 #14559701

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Subgroups

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

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2432

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7268, C₁₉×#7278, C₁₉×#7371, …
maximal normal subgroup of	C₁₉×#7268, C₁₉×#7278, C₁₉×#7371, …
maximal quotient of	C₁₉×#8805, C₁₉×#8809, C₁₉×#8813, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 576);