C₁₉×#1794 #14559651

order	2432
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#1794

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#120
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#379
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₂×C₄ ▷ 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)(20,21,25,29,26,30,24,37)(22,31,33,27,34,42,38,41)(23,28,35,44,36,45,39,43)(32,47,50,51,49,46,48,40);(20,22)(21,27)(23,32)(24,38)(25,33)(26,34)(28,40)(29,42)(30,41)(31,37)(35,50)(36,49)(39,48)(43,46)(44,47)(45,51);(20,23)(21,28)(22,32)(24,39)(25,35)(26,36)(27,40)(29,44)(30,45)(31,46)(33,50)(34,49)(37,43)(38,48)(41,51)(42,47)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7346, C₁₉×#7347, C₁₉×#13045, …
maximal normal subgroup of	C₁₉×#7346, C₁₉×#7347, C₁₉×#13045, …
maximal quotient of	C₁₉×#8318, C₁₉×#8319, C₁₉×#8320, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 526);