C₁₉×#2012 #14559869

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2012

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

426 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 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)(29,32)(30,34)(33,35);(21,23)(24,25)(26,27)(28,29,31,33)(30,35,34,32);(25,27)(28,29)(30,35)(31,33)(32,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2012, C₁₉×#23421, C₁₉×#23422, …
maximal normal subgroup of	C₂×C₁₉×#2012, C₁₉×#23421, C₁₉×#23422, …
maximal quotient of	C₁₉×#9947, C₁₉×#9948, C₁₉×#9950, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 744);