C₁₉×#1903 #14559760

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1902
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1903

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#386
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 324 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) = 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)(20,21,26,29)(22,25,28,24)(23,30)(27,31)(32,34)(33,35);(20,22,24,21,26,28,25,29)(23,30,32,27,33,35,31,34);(20,23)(21,27)(22,30)(24,32)(25,31)(26,33)(28,35)(29,34)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1903, C₁₉×#20995, C₁₉×#22284, …
maximal normal subgroup of	C₂×C₁₉×#1903, C₁₉×#20995, C₁₉×#22284, …
maximal quotient of	C₁₉×#9089, C₁₉×#9090, C₁₉×#9093, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 635);