C₁₉×#2896 #14560753

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2896

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×#41×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,33)(27,32)(28,36)(29,31)(30,34)(35,39)(37,38);(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36);(25,31)(30,38)(32,36)(33,39);(24,27,29,28)(25,32,31,36)(26,34,35,37)(30,39,38,33)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10772, C₁₉×#10778, C₁₉×#10782, …
maximal normal subgroup of	C₁₉×#10772, C₁₉×#10778, C₁₉×#10782, …
maximal quotient of	C₁₉×#17437, C₁₉×#17447, C₁₉×#17450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1628);

C19×#2896 #14560753

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2896 #14560753