C₃×C₃⋊(C₃⋊(C₅⋊D₅)) #13062549

order	1350
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₅⋊D₅))
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃×C₃⋊(C₃⋊(C₅⋊D₅))
unambiguous semidirect product	C₃⋊(C₃×C₃⋊(C₅⋊D₅))
unambiguous semidirect product	C₅⋊(C₃×C₃⋊D₁₅)

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊(C₅⋊D₅))
commutator, cosocle, hypocenter	C₃²×C₅²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃³×C₅²	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₃

256 conjugacy classes of subgroups.

μ_t(G) = 450

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

maximal subgroup of	C₃×C₃⋊D₃×C₅⋊D₅, D₃×C₃⋊(C₃⋊(C₅⋊D₅)), #72222444, …
maximal normal subgroup of	C₃×C₃⋊D₃×C₅⋊D₅, D₃×C₃⋊(C₃⋊(C₅⋊D₅)), #72222444, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 108);