C₁₉×#2016 #14559873

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2016

Subgroups

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

370 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(28,29,34,38)(30,39,31,42)(32,37,33,36)(35,41,43,40);(21,23)(24,25)(26,27)(28,30,34,31)(29,35,38,43)(32,41,33,40)(36,42,37,39);(25,27)(28,31,34,30)(29,35,38,43)(32,40,33,41)(36,42,37,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7405, C₁₉×#7756, C₁₉×#7757, …
maximal normal subgroup of	C₁₉×#7405, C₁₉×#7756, C₁₉×#7757, …
maximal quotient of	C₁₉×#9957, C₁₉×#9959, C₁₉×#9967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 748);