C₁₉×#1829 #14559686

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1829

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#381
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 304

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12725, C₁₉×#12726, C₂×C₁₉×#1829, …
maximal normal subgroup of	C₁₉×#12725, C₁₉×#12726, C₂×C₁₉×#1829, …
maximal quotient of	C₁₉×#8734, C₁₉×#8736, C₁₉×#8751, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 561);

C19×#1829 #14559686

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1829 #14559686