C₁₉×#1923 #14559780

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1923

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

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)(22,23)(25,26)(28,29,31,34,32,30,33,35);(24,25,27,26)(28,30,31,35,32,29,33,34);(21,23)(24,26,27,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₉×#1923, C₁₉×#21046, C₁₉×#21048, …
maximal normal subgroup of	C₂×C₁₉×#1923, C₁₉×#21046, C₁₉×#21048, …
maximal quotient of	C₁₉×#9541, C₁₉×#9542, C₁₉×#9543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 655);

C19×#1923 #14559780