C₁₉×#1943 #14559800

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1943

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

240 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 35
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12955, C₁₉×#13118, C₁₉×#13153, …
maximal normal subgroup of	C₁₉×#12955, C₁₉×#13118, C₁₉×#13153, …
maximal quotient of	C₁₉×#9595, C₁₉×#9599, C₁₉×#9617, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 675);