C₁₉×#2183 #14560040

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2183

Subgroups

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

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,25)(24,26)(28,29,31,35,32,30,37,38,33,36,40,43,41,39,34,42);(20,22,24,23)(21,25,26,27);(20,23,24,22)(21,25,26,27)(28,30,31,38,32,36,37,43,33,39,40,42,41,29,34,35)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7393, C₁₉×#12049, C₁₉×#12051, …
maximal normal subgroup of	C₁₉×#7393, C₁₉×#12049, C₁₉×#12051, …
maximal quotient of	C₁₉×#12662, C₁₉×#12663, C₁₉×#13104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 915);

C19×#2183 #14560040