D₃×C₄₁×C₅₃ #27189339

order	13038
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₁×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₄₁×C₅₃
unambiguous semidirect product	C₃⋊(C₂×C₄₁×C₅₃)

Splittings

Fitting, socle, Hall	C₃×C₄₁×C₅₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄₁×C₅₃
Hall	C₃×C₅₃ ⋊ C₂×C₄₁
Hall	C₃×C₄₁ ⋊ C₂×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁×C₅₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₄₁×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₅₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₁×C₅₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 6519

A minimal faithful permutation representation — 2 generators on 97 points:

(2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,2,3)

Conjugacy classes & character table

6519 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₄₁×D₅₃, D₃×C₅₃×D₄₁, D₃×D₂₁₇₃, …
maximal normal subgroup of	D₃×C₄₁×D₅₃, D₃×C₅₃×D₄₁, D₃×D₂₁₇₃, …
maximal quotient of	Dic₃×C₄₁×C₅₃, C₂×D₃×C₄₁×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13038, 5);

D3×C41×C53 #27189339