C₁₉×#2437 #14560294

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2437

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12120, C₁₉×#12214, C₂×C₁₉×#2437, …
maximal normal subgroup of	C₁₉×#12120, C₁₉×#12214, C₂×C₁₉×#2437, …
maximal quotient of	C₁₉×#13877, C₁₉×#13980, C₁₉×#14004, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1169);

C19×#2437 #14560294

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2437 #14560294