C₁₉×#2165 #14560022

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2165

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#432
prime radical	C₂³×C₁₉	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₁₉×#97 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7225, C₁₉×#7226, C₁₉×#11521, …
maximal normal subgroup of	C₁₉×#7225, C₁₉×#7226, C₁₉×#11521, …
maximal quotient of	C₁₉×#12595, C₁₉×#12607, C₁₉×#12659, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 897);

C19×#2165 #14560022

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2165 #14560022