C₃×C₁₁×D₁₉ #11929419

order	1254
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₁₁×D₁₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 627

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₁₁×D₁₉, D₃×C₁₁×D₁₉, D₁₉×D₃₃, …
maximal normal subgroup of	C₃×D₁₁×D₁₉, D₃×C₁₁×D₁₉, D₁₉×D₃₃, …
maximal quotient of	C₃×C₁₁×Dic₁₉, C₂×C₃×C₁₁×D₁₉, C₉×C₁₁×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 5);

C3×C11×D19 #11929419