C₃²×C₃⋊(C₅⋊D₅) #13062546

order	1350
isoclinism	isoclinic class of C₃⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃²×C₃⋊(C₅⋊D₅)
unambiguous semidirect product	C₃⋊(C₃²×C₅⋊D₅)
unambiguous semidirect product	C₅⋊(C₃²×D₁₅)

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

256 conjugacy classes of subgroups.

μ_t(G) = 450

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

maximal subgroup of	C₃²×D₃×C₅⋊D₅, C₃⋊D₃×C₃⋊(C₅⋊D₅), #72222444, …
maximal normal subgroup of	C₃²×D₃×C₅⋊D₅, C₃⋊D₃×C₃⋊(C₅⋊D₅), #72222444, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 105);