C₁₉×#1801 #14559658

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1801

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

272 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 124 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)(21,23)(24,25,27,31,28,30,36,38)(26,32,33,39,34,29,35,37);(20,21,22,23);(24,26,28,34)(25,29,30,32)(27,35,36,33)(31,39,38,37)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7238, C₁₉×#7323, C₁₉×#8354, …
maximal normal subgroup of	C₁₉×#7238, C₁₉×#7323, C₁₉×#8354, …
maximal quotient of	C₁₉×#8558, C₁₉×#8560, C₁₉×#8562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 533);