C₁₉×#1630 #14559487

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1630

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29,33,36)(30,37,39,42)(31,35,32,40)(34,41,43,38);(22,26)(24,27)(28,30)(29,34)(31,38)(32,41)(33,39)(35,42)(36,43)(37,40);(20,21)(22,27)(23,25)(24,26)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7518, C₁₉×#13676, C₂×C₁₉×#1630, …
maximal normal subgroup of	C₁₉×#7518, C₁₉×#13676, C₂×C₁₉×#1630, …
maximal quotient of	C₁₉×#7751, C₁₉×#7755, C₁₉×#7779, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 362);