C₁₉×C₃⋊D₃₃ #16836795

order	3762
isoclinism	isoclinic class of C₃⋊D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₉×C₃⋊D₃₃
unambiguous semidirect product	C₃⋊(C₁₉×D₃₃)
unambiguous semidirect product	C₁₁⋊(C₃⋊D₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₁₉ ⋊ C₂
derived, Hall	C₃²×C₁₁ ⋊ C₂×C₁₉
Hall	C₁₁×C₁₉ ⋊ C₃⋊D₃
Hall	C₃²×C₁₉ ⋊ D₁₁
Sylow	C₁₁ ⋊ C₃⋊D₃×C₁₉
Sylow	C₃² ⋊ C₁₉×D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₉	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1881

A minimal faithful permutation representation — 3 generators on 36 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(23,24)(25,26)(27,28)(29,30)(32,33)(35,36);(20,21,23,25,27,29,30,28,26,24,22)(34,35,36);(31,32,33)

Conjugacy classes & character table

969 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×C₃⋊(C₃⋊AGL(1,𝔽₁₁)), C₁₉×C₃⋊D₁₆₅, C₅×C₁₉×C₃⋊D₃₃, …
maximal normal subgroup of	C₁₉×C₃⋊(C₃⋊AGL(1,𝔽₁₁)), C₅×C₁₉×C₃⋊D₃₃, C₇×C₁₉×C₃⋊D₃₃
maximal quotient of	C₁₉×C₃⋊D₁₆₅, C₅×C₁₉×C₃⋊D₃₃, C₇×C₁₉×C₃⋊D₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 35);

C19×C3⋊D33 #16836795