C₁₉×#1645 #14559502

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

Aliases

direct product

C₁₉×#1645

Subgroups

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

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

normal subgroups only

This group has 200 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) = 2432

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)(28,29,32,35)(30,36,37,43)(31,39,40,34)(33,41,42,38);(20,21,23,25)(22,27,26,24)(31,40)(34,39)(36,43)(38,41);(28,30,32,37)(29,33,35,42)(31,41,40,38)(34,43,39,36)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1645, C₁₉×#18515, C₁₉×#18518, …
maximal normal subgroup of	C₂×C₁₉×#1645, C₁₉×#18515, C₁₉×#18518, …
maximal quotient of	C₁₉×#7759, C₁₉×#7761, C₁₉×#7766, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 377);