C₁₉×#2360 #14560217

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2360

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

620 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)(21,23)(24,25,27,26)(28,29)(30,31)(32,33)(34,35);(24,26,27,25)(29,33)(31,34);(20,21)(22,23)(28,30)(29,34)(31,33)(32,35);(28,31,32,34)(29,30,33,35)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#22854, C₁₉×#22859, C₁₉×#22862, …
maximal normal subgroup of	C₁₉×#22854, C₁₉×#22859, C₁₉×#22862, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₁₉, C₁₉×#13814, C₁₉×#13817, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1092);

C19×#2360 #14560217

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2360 #14560217