C₁₉×#1937 #14559794

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1937

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

230 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1937, C₁₉×#21098, C₁₉×#21099, …
maximal normal subgroup of	C₂×C₁₉×#1937, C₁₉×#21098, C₁₉×#21099, …
maximal quotient of	C₁₉×#9553, C₁₉×#9554, C₁₉×#9559, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 669);