C₁₃⋊C₃×C₄₁ #13097647

order	1599
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₃×C₄₁
unambiguous semidirect product	C₁₃⋊(C₃×C₄₁)
unambiguous semidirect product	(C₁₃×C₄₁)⋊C₃

Splittings

Fitting, socle, Hall	C₁₃×C₄₁ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₄₁	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 533

A minimal faithful permutation representation — 2 generators on 54 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(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);(1,2,4,3,6,10,7,11,13,5,8,12,9)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₃⋊C₃×C₄₁, C₁₃⋊C₃×D₄₁, C₄₁×D₁₃⋊C₃, …
maximal normal subgroup of	C₂×C₁₃⋊C₃×C₄₁, C₁₃⋊C₃×D₄₁, C₄₁×D₁₃⋊C₃, …
maximal quotient of	C₂×C₁₃⋊C₃×C₄₁, C₄₁×C₁₃⋊C₉, C₃×C₁₃⋊C₃×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1599, 1);

C13⋊C3×C41 #13097647