C₁₃×C₃₁×D₄₅ #49136502

order	36270
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₃₁×D₄₅
unambiguous semidirect product	C₅⋊(C₁₃×D₉×C₃₁)
unambiguous semidirect product	C₉⋊(D₅×C₁₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₁₃×C₃₁	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₁₃×C₃₁
Frattini	C₃	C₁₃×D₁₅×C₃₁
Fitting	C₅×C₉×C₁₃×C₃₁	C₂
socle	C₃×C₅×C₁₃×C₃₁	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₁₃×C₃₁

48 conjugacy classes of subgroups.

μ_t(G) = 18135

9672 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 22);