C₁₉×#1375 #14559232

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1375

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₄²
commutator	C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#97
prime radical	C₂³×C₁₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7109, C₁₉×#7116, C₁₉×#7117, …
maximal normal subgroup of	C₁₉×#7109, C₁₉×#7116, C₁₉×#7117, …
maximal quotient of	C₁₉×#7137, C₁₉×#7142, C₁₉×#7145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 107);

C19×#1375 #14559232

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1375 #14559232