C₁₉×#2344 #14560201

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2344

Subgroups

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

604 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)(20,21,23,22)(24,25,26,27)(30,34)(32,35);(21,22)(28,29,31,33)(30,32,34,35);(28,30)(29,32)(31,34)(33,35);(20,22,23,21)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9256, C₁₉×#9260, C₁₉×#22406, …
maximal normal subgroup of	C₁₉×#9256, C₁₉×#9260, C₁₉×#22406, …
maximal quotient of	C₁₉×#13799, C₂²⋊C₄×C₄⋊C₄×C₁₉, C₁₉×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1076);

C19×#2344 #14560201

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2344 #14560201