C₁₉×#2352 #14560209

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×#2352

Subgroups

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

660 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)(24,25,26,27)(29,30)(33,34);(21,23)(28,29,32,30)(31,34,35,33);(28,30,32,29)(31,34,35,33);(20,21)(22,23)(28,31)(29,33)(30,34)(32,35)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#22414, C₁₉×#22416, C₁₉×#22420, …
maximal normal subgroup of	C₁₉×#22414, C₁₉×#22416, C₁₉×#22420, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₁₉, C₁₉×#13801, C₁₉×#13804, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1084);

C19×#2352 #14560209

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2352 #14560209