C₁₉×#1945 #14559802

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1945

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 208 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)(20,21)(22,23)(24,25,29,33,30,34,28,38)(26,31,35,39,36,32,27,37);(21,23)(24,26,29,35,30,36,28,27)(25,31,33,39,34,32,38,37);(24,27,28,36,30,35,29,26)(25,32,33,37,34,31,38,39)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7119, C₁₉×#12939, C₁₉×#12951, …
maximal normal subgroup of	C₁₉×#7119, C₁₉×#12939, C₁₉×#12951, …
maximal quotient of	C₁₉×#9593, C₁₉×#9594, C₁₉×#9599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 677);