C₃×C₄₁×D₁₅₅ #49185757

order	38130
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₄₁×D₁₅₅
unambiguous semidirect product	C₅⋊(C₃×C₄₁×D₃₁)

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₁×C₄₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₃×C₄₁

32 conjugacy classes of subgroups.

μ_t(G) = 19065

9717 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 20);