C₁₉×#2064 #14559921

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2064

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 84 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 — 3 generators on 39 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2064, C₁₉×#23601, C₁₉×#23603, …
maximal normal subgroup of	C₂×C₁₉×#2064, C₁₉×#23601, C₁₉×#23603, …
maximal quotient of	C₁₉×#10588, C₁₉×#10590, C₁₉×#10592, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 796);