C₁₉×#2102 #14559959

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2102

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#400
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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)(20,21,24,23,25,27,29,33)(22,28,30,35,31,32,34,26);(20,22,29,30,25,31,24,34)(21,26,33,28,27,35,23,32);(20,23,24,27,25,33,29,21)(22,28,30,35,31,32,34,26)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7440, C₁₉×#7441, C₁₉×#12307, …
maximal normal subgroup of	C₁₉×#7440, C₁₉×#7441, C₁₉×#12307, …
maximal quotient of	C₁₉×#10687, C₁₉×#10688, C₁₉×#10689, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 834);