C₁₉×#1836 #14559693

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1836

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 224 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) = 2432

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7266, C₁₉×#7367, C₁₉×#8911, …
maximal normal subgroup of	C₁₉×#7266, C₁₉×#7367, C₁₉×#8911, …
maximal quotient of	C₁₉×#8786, C₁₉×#8789, C₁₉×#8794, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 568);