C₁₉×#1637 #14559494

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

Aliases

direct product

C₁₉×#1637

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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)(20,21,23,26)(22,24,27,25)(28,29,34,38)(30,39,31,42)(32,37,33,36)(35,41,43,40);(21,24)(22,27)(25,26)(28,30,34,31)(29,35,38,43)(32,41,33,40)(36,42,37,39);(28,31,34,30)(29,35,38,43)(32,40,33,41)(36,42,37,39)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1637, C₁₉×#18494, C₁₉×#18517, …
maximal normal subgroup of	C₂×C₁₉×#1637, C₁₉×#18494, C₁₉×#18517, …
maximal quotient of	C₁₉×#7764, C₁₉×#7766, C₁₉×#7772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 369);