C₁₉×#1950 #14559807

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1950

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	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

200 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 1216

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)(21,23)(24,25,28,31,29,32,27,36)(26,33,34,30,35,38,37,39);(24,26,28,34,29,35,27,37)(25,30,31,38,32,39,36,33);(20,21,22,23)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8906, C₁₉×#8907, C₁₉×#8908, …
maximal normal subgroup of	C₁₉×#8906, C₁₉×#8907, C₁₉×#8908, …
maximal quotient of	C₁₉×#9601, C₁₉×#9602, C₁₉×#9603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 682);