C₁₉×#1931 #14559788

order	2432
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1931

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 232 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)(20,21,23,22)(25,29)(26,33)(27,30)(31,38)(32,36)(35,39);(20,22,23,21)(24,25,30,36,28,32,27,29)(26,31,37,38,33,39,34,35);(24,26,27,34,28,33,30,37)(25,31,29,35,32,39,36,38)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1931, C₁₉×#21075, C₁₉×#21076, …
maximal normal subgroup of	C₂×C₁₉×#1931, C₁₉×#21075, C₁₉×#21076, …
maximal quotient of	C₁₉×#9550, C₁₉×#9552, C₁₉×#9563, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 663);