C₁₉×#1890 #14559747

order	2432
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1890

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

386 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 112 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)(21,23)(24,25)(26,29)(27,34,35,30)(28,31)(32,36,38,39)(33,37);(20,21,22,23)(24,26,28,33)(25,29,31,37)(27,32,35,38)(30,36,34,39);(24,27)(25,30)(26,32)(28,35)(29,36)(31,34)(33,38)(37,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12754, C₁₉×#12760, C₁₉×#12761, …
maximal normal subgroup of	C₁₉×#12754, C₁₉×#12760, C₁₉×#12761, …
maximal quotient of	C₁₉×#8966, C₁₉×#8968, C₁₉×#9011, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 622);