C₁₉×#1335 #14559192

order	2432
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1335

Subgroups

	subgroup	G/H
center	C₈×C₁₉	D₈
commutator	C₈	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂²×C₁₉
socle	C₂×C₁₉	D₄⋊C₈
prime radical	C₁₉×#135	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1335, C₁₉×#11602, C₁₉×#11669, …
maximal normal subgroup of	C₂×C₁₉×#1335, C₁₉×#11602, C₁₉×#11669, …
maximal quotient of	C₁₉×#7068, C₁₉×#7069, C₁₉×#7074, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 67);

C19×#1335 #14559192

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1335 #14559192