C₁₉×#3343 #14561200

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

Aliases

direct product

C₁₉×#3343

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

376 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)(29,32)(30,34)(33,35);(20,22)(21,25)(23,26)(24,27)(29,33)(32,35);(20,23,24,21)(22,26,27,25)(28,29)(30,35)(31,33)(32,34);(22,27)(25,26)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#3343, C₁₉×#61243, C₁₉×#61252, …
maximal normal subgroup of	C₂×C₁₉×#3343, C₁₉×#61243, C₁₉×#61252, …
maximal quotient of	C₁₉×#22491, C₁₉×#22495, C₁₉×#22617, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2075);

C19×#3343 #14561200

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3343 #14561200