C₁₉×#1812 #14559669

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

Aliases

direct product

C₁₉×#1812

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#380
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 260 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) = 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)(23,34,36,27)(24,37)(25,29)(26,32)(28,38)(31,44,46,42)(33,43)(35,41,50,49)(39,45,48,51)(40,47);(20,22,24,32,25,33,38,47)(21,26,28,30,29,40,37,43)(23,31,35,45,36,46,50,51)(27,39,41,42,34,48,49,44);(20,23)(21,27)(22,31)(24,35)(25,36)(26,39)(28,41)(29,34)(30,42)(32,45)(33,46)(37,49)(38,50)(40,48)(43,44)(47,51)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7227, C₁₉×#7228, C₁₉×#11867, …
maximal normal subgroup of	C₁₉×#7227, C₁₉×#7228, C₁₉×#11867, …
maximal quotient of	C₁₉×#8601, C₁₉×#8602, C₁₉×#8603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 544);