C₁₉×#1422 #14559279

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₁₉	D₄
commutator	C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	C₄⋊C₁₆
prime radical	C₂²×C₁₉	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ G

58 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)(20,21,24,30,25,31,39,46,26,29,40,44,36,45,49,51,27,32,41,47,34,28,42,43,23,37,38,50,22,33,35,48);(20,22,23,34,27,36,26,25)(21,28,29,33,32,31,37,45)(24,35,38,42,41,49,40,39)(30,43,44,48,47,46,50,51)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7381, C₁₉×#7382, C₁₉×#7447, …
maximal normal subgroup of	C₁₉×#7381, C₁₉×#7382, C₁₉×#7447, …
maximal quotient of	C₁₉×#7455, C₁₉×#7458, C₁₉×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 154);

C19×#1422 #14559279