C₁₉×#1915 #14559772

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1915

Subgroups

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

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

normal subgroups only

This group has 308 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)(20,21,24,29,25,28,30,43)(22,26,33,40,32,41,37,44)(23,34,36,45,35,27,38,42)(31,39,47,50,46,49,48,51);(20,22,30,33,25,32,24,37)(21,26,29,44,28,41,43,40)(23,31,36,48,35,46,38,47)(27,39,45,50,34,49,42,51);(20,23)(21,27)(22,31)(24,38)(25,35)(26,39)(28,34)(29,45)(30,36)(32,46)(33,48)(37,47)(40,51)(41,49)(42,43)(44,50)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12757, C₁₉×#12758, C₁₉×#12770, …
maximal normal subgroup of	C₁₉×#12757, C₁₉×#12758, C₁₉×#12770, …
maximal quotient of	C₁₉×#9108, C₁₉×#9110, C₁₉×#9189, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 647);