C₁₉×#2628 #14560485

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2628

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(24,25)(26,29)(27,28)(30,31)(32,33,36,39)(34,37,38,35);(21,23)(25,28)(29,30)(32,34)(33,37)(35,39)(36,38);(20,21)(22,23)(24,25)(26,30)(27,28)(29,31)(32,35,36,37)(33,38,39,34);(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9191, C₁₉×#9192, C₁₉×#9193, …
maximal normal subgroup of	C₁₉×#9191, C₁₉×#9192, C₁₉×#9193, …
maximal quotient of	C₁₉×#14264, C₁₉×#14266, C₁₉×#14277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1360);

C19×#2628 #14560485

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2628 #14560485