C₄×C₁₉×#131 #14560731

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₄×C₁₉×#131

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₉	C₂²
commutator	C₂	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₉ ◁ G

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6,8,11,9,12,15,18)(7,10,14,17,13,16,19,20);(5,7)(6,10)(8,14)(9,13)(11,17)(12,16)(15,19)(18,20);(7,13)(10,16)(14,19)(17,20)

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#8184, C₁₉×#8185, C₁₉×#8186, …
maximal normal subgroup of	C₁₉×#8184, C₁₉×#8185, C₁₉×#8186, …
maximal quotient of	C₈×C₁₉×#131, C₁₉×#17320, C₁₉×#17328, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1606);

C4×C19×#131 #14560731