C₅×C₁₁⋊(C₁₃⋊D₁₃) #32915775

order	18590
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₅×C₁₁⋊(C₁₃⋊D₁₃)
unambiguous semidirect product	C₁₃⋊(C₅×D₁₄₃)

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₁₃² ⋊ C₂
derived, Hall	C₁₁×C₁₃² ⋊ C₂×C₅
Hall	C₅×C₁₃² ⋊ D₁₁
Sylow	C₁₃² ⋊ C₅×D₁₁
Hall	C₅×C₁₁ ⋊ C₁₃⋊D₁₃
Sylow	C₁₁ ⋊ C₅×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊(C₁₃⋊D₁₃)
commutator, cosocle, hypocenter	C₁₁×C₁₃²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₃²	C₂
LCS	G ▷ C₁₁×C₁₃²
UCS	C₁ ◁ C₅

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 9295

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42);(6,7,9,11,13,15,16,14,12,10,8)(30,31,33,35,37,39,41,42,40,38,36,34,32);(17,18,20,22,24,26,28,29,27,25,23,21,19)

Conjugacy classes & character table

4655 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₁₃×D₁₄₃, C₅×D₁₁×C₁₃⋊D₁₃, D₆₅⋊D₁₄₃, …
maximal normal subgroup of	C₅×D₁₃×D₁₄₃, C₅×D₁₁×C₁₃⋊D₁₃, D₆₅⋊D₁₄₃, …
maximal quotient of	C₅×C₁₁⋊#10621725, C₂×C₅×C₁₁⋊(C₁₃⋊D₁₃)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18590, 26);

C5×C11⋊(C13⋊D13) #32915775