C₁₉×#1418 #14559275

order	2432
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1418

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#357
commutator	C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₉
prime radical	C₁₉×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26,27,42)(22,30)(23,35)(24,37)(28,46,45,50)(29,47,39,44)(31,36,43,41)(32,38)(33,51)(34,40)(48,49);(20,21)(22,31)(23,36)(24,39)(25,27)(26,40)(28,35)(29,37)(30,42)(32,45)(33,46)(34,43)(38,41)(44,49)(47,51)(48,50)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1418, C₁₉×#13622, C₁₉×#13657, …
maximal normal subgroup of	C₂×C₁₉×#1418, C₁₉×#13622, C₁₉×#13657, …
maximal quotient of	C₁₉×#7385, C₁₉×#7386, C₁₉×#7418, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 150);

C19×#1418 #14559275

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1418 #14559275