C₁₉×#1902 #14559759

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1902
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1902

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#386
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

304 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 108 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)(22,31)(23,35,38,45)(24,39)(25,29)(26,30)(27,33)(28,37,44,36)(32,47,49,41)(34,42)(40,43)(46,48,51,50);(20,22,24,33,26,34,25,40)(21,27,29,31,30,43,39,42)(23,32,37,50,38,49,36,48)(28,41,45,46,44,47,35,51);(20,23)(21,28)(22,32)(24,37)(25,36)(26,38)(27,41)(29,45)(30,44)(31,46)(33,50)(34,49)(35,39)(40,48)(42,51)(43,47)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1902, C₁₉×#20995, C₁₉×#22284, …
maximal normal subgroup of	C₂×C₁₉×#1902, C₁₉×#20995, C₁₉×#22284, …
maximal quotient of	C₁₉×#9087, C₁₉×#9088, C₁₉×#9091, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 634);