C₁₉×#1624 #14559481

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1624

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1216

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)(21,25)(22,23)(26,27)(29,32)(30,34)(33,35);(20,21,24,26)(22,25,23,27)(30,34)(32,35);(20,22,24,23)(21,25,26,27)(28,29,31,33)(30,35,34,32)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7519, C₁₉×#13681, C₂×C₁₉×#1624, …
maximal normal subgroup of	C₁₉×#7519, C₁₉×#13681, C₂×C₁₉×#1624, …
maximal quotient of	C₁₉×#7742, C₁₉×#7743, C₁₉×#7746, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 356);