C₃×C₅×C₁₃×ΓL(1,𝔽₃₂) #44475233

order	30225
automorphism	?
homology	Abelianization (H₁) = C₃×C₅²×C₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₃×C₅×C₁₃×ΓL(1,𝔽₃₂)
unambiguous semidirect product	(C₃×C₃₁)⋊(C₅²×C₁₃)
unambiguous semidirect product	(C₃×C₅×C₃₁)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₃×C₁₃×C₃₁)⋊C₅²
unambiguous semidirect product	(C₃×C₅×C₁₃×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₃×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₅×C₁₃

64 conjugacy classes of subgroups.

μ_t(G) = 6045

2145 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30225, 16);