C₁₉×#1398 #14559255

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#1398

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₄²
commutator	C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	#346
prime radical	C₂²×C₁₉	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ G

60 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)(20,21,22,27,23,29,32,42,24,30,33,40,34,44,46,50,25,28,31,41,35,43,45,51,36,26,37,38,47,39,48,49);(21,26,28,30)(22,31)(27,40,41,38)(29,39,43,44)(32,45)(33,37)(42,50,51,49)(46,48)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7333, C₁₉×#7389, C₁₉×#7390, …
maximal normal subgroup of	C₁₉×#7333, C₁₉×#7389, C₁₉×#7390, …
maximal quotient of	C₁₉×#7330, C₁₉×#7332, C₁₉×#7466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 130);

C19×#1398 #14559255

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1398 #14559255