C₁₉×#1833 #14559690

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1833

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#382
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₁₉×#117 ◁ G

172 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 100 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)(22,30,33,26)(23,34,36,49)(24,29)(25,28)(27,35,40,50)(31,44)(32,43,47,39)(37,41)(38,45)(42,51)(46,48);(20,22,24,32,25,33,37,47)(21,26,29,39,28,30,41,43)(23,31,35,45,36,46,50,51)(27,38,34,48,40,42,49,44);(20,23)(21,27,28,40)(22,31)(24,35)(25,36)(26,38,30,42)(29,34,41,49)(32,45)(33,46)(37,50)(39,48,43,44)(47,51)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12826, C₁₉×#12827, C₁₉×#12828, …
maximal normal subgroup of	C₁₉×#12826, C₁₉×#12827, C₁₉×#12828, …
maximal quotient of	C₁₉×#8780, C₁₉×#8781, C₁₉×#8782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 565);