C₁₉×#1925 #14559782

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1925

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

290 conjugacy classes of subgroups.

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1925, C₁₉×#21058, C₁₉×#21059, …
maximal normal subgroup of	C₂×C₁₉×#1925, C₁₉×#21058, C₁₉×#21059, …
maximal quotient of	C₁₉×#9541, C₁₉×#9545, C₁₉×#9561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 657);

C19×#1925 #14559782

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1925 #14559782