C₁₉×#2681 #14560538

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2681

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#36716, C₁₉×#36718, C₁₉×#36719, …
maximal normal subgroup of	C₁₉×#36716, C₁₉×#36718, C₁₉×#36719, …
maximal quotient of	C₁₉×#14360, C₁₉×#14361, C₁₉×#14362, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1413);

C19×#2681 #14560538

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2681 #14560538