C₂×C₃₁×C₃⋊(C₃⋊(C₅⋊D₅)) #42124995

order	27900
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₅⋊D₅))
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₁ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₃₁×C₃⋊(C₃⋊(C₅⋊D₅))
unambiguous semidirect product	(C₂×C₃)⋊(C₃₁×C₃⋊(C₅⋊D₅))
unambiguous semidirect product	(C₂×C₅)⋊(C₃₁×C₃⋊D₁₅)

	subgroup	G/H
center, hypercenter	C₂×C₃₁	C₃⋊(C₃⋊(C₅⋊D₅))
commutator, cosocle, hypocenter	C₃²×C₅²	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₃₁	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂×C₃₁

480 conjugacy classes of subgroups.

7068 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 742);