C₁₉×#1791 #14559648

order	2432
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#1791

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#120
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#379
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,37,42)(22,30,33,43,32,26,36,39)(23,27,35,40,34,41,47,51)(31,38,46,49,45,44,48,50);(20,22)(21,26)(23,31)(24,36)(25,32)(27,38)(28,30)(29,43)(33,37)(34,45)(35,48)(39,42)(40,50)(41,44)(46,47)(49,51);(20,23)(21,27)(22,31)(24,35)(25,34)(26,38)(28,41)(29,40)(30,44)(32,45)(33,46)(36,48)(37,47)(39,49)(42,51)(43,50)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13045, C₁₉×#13046, C₁₉×#13051, …
maximal normal subgroup of	C₁₉×#13045, C₁₉×#13046, C₁₉×#13051, …
maximal quotient of	C₁₉×#8316, C₁₉×#8317, C₁₉×#8348, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 523);