C₁₉×#1888 #14559745

order	2432
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1888

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

344 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 608

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7481, C₁₉×#7489, C₁₉×#12774, …
maximal normal subgroup of	C₁₉×#7481, C₁₉×#7489, C₁₉×#12774, …
maximal quotient of	C₁₉×#8960, C₁₉×#8964, C₁₉×#9002, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 620);