C₁₉×#1816 #14559673

order	2432
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1816

Subgroups

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

264 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 120 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)(20,21)(22,23)(24,25,29,32,30,27,28,38)(26,33,36,34,37,39,35,31);(24,26,29,36,30,37,28,35)(25,31,38,39,27,34,32,33);(21,23)(24,27)(25,30)(26,34)(28,38)(29,32)(31,37)(33,36)(35,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12748, C₁₉×#12749, C₁₉×#12842, …
maximal normal subgroup of	C₁₉×#12748, C₁₉×#12749, C₁₉×#12842, …
maximal quotient of	C₁₉×#8605, C₁₉×#8606, C₁₉×#8627, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 548);