C₁₉×#1778 #14559635

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1778

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12651, C₁₉×#12678, C₁₉×#13114, …
maximal normal subgroup of	C₁₉×#12651, C₁₉×#12678, C₁₉×#13114, …
maximal quotient of	C₁₉×#8275, C₁₉×#8276, C₁₉×#8277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 510);

C19×#1778 #14559635

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1778 #14559635