C₁₉×#3386 #14561243

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3386

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×D₄×C₁₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#19764, C₁₉×#19767, C₁₉×#19812, …
maximal normal subgroup of	C₁₉×#19764, C₁₉×#19767, C₁₉×#19812, …
maximal quotient of	C₁₉×#22523, C₁₉×#22524, C₁₉×#22671, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2118);

C19×#3386 #14561243

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3386 #14561243