C₃×C₄₁×C₂²⋊(C₅²⋊C₃) #49147201

order	36900
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₁ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₃×C₄₁×C₂²⋊(C₅²⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₄₁×C₅²⋊C₃)
unambiguous semidirect product	(C₃×C₅²)⋊(A₄×C₄₁)
unambiguous semidirect product	(C₂²×C₃×C₄₁)⋊(C₅²⋊C₃)
unambiguous semidirect product	(C₃×C₅²×C₄₁)⋊A₄

	subgroup	G/H
center, hypercenter	C₃×C₄₁	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₅²	C₃²×C₄₁
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅²×C₄₁	C₃
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₃×C₄₁

96 conjugacy classes of subgroups.

μ_t(G) = 3690

4428 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 602);