C₁₉×#3150 #14561007

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#3150

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

564 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9007, C₁₉×#10032, C₁₉×#10034, …
maximal normal subgroup of	C₁₉×#9007, C₁₉×#10032, C₁₉×#10034, …
maximal quotient of	C₁₉×#19608, C₁₉×#19613, C₁₉×#19616, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1882);