C₁₉×#1369 #14559226

order	2432
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#1369

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#106
commutator	C₈	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂²×C₁₉
socle	C₂×C₁₉	#334
prime radical	C₂²×C₁₉	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×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)(20,21,24,30,26,31,41,47,27,32,40,29,25,43,23,39)(22,33,35,44,37,48,34,45,38,46,42,51,36,50,49,28);(20,22,23,34,25,36,40,35,27,38,41,49,26,37,24,42)(21,28,29,33,31,44,39,48,32,45,30,46,43,51,47,50)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7390, C₁₉×#7391, C₁₉×#7457, …
maximal normal subgroup of	C₁₉×#7390, C₁₉×#7391, C₁₉×#7457, …
maximal quotient of	C₁₉×#7099, C₁₉×#7161, C₂×C₁₉×#1369

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 101);

C19×#1369 #14559226

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1369 #14559226