C₁₉×#1899 #14559756

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#1899

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 378 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)(26,29,33,36)(27,30)(28,31)(32,35,38,39)(34,37);(24,26)(25,29,31,36)(27,32)(28,33)(30,35,37,39)(34,38);(21,23)(24,27,28,34)(25,30,31,37)(26,32,33,38)(29,35,36,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8487, C₁₉×#8488, C₂×C₁₉×#1899, …
maximal normal subgroup of	C₁₉×#8487, C₁₉×#8488, C₂×C₁₉×#1899, …
maximal quotient of	C₁₉×#9080, C₁₉×#9082, C₁₉×#9084, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 631);