C₁₉²×C₅²⋊C₃ #41028869

order	27075
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉² · Schur multiplier (H₂) = C₅×C₁₉

Aliases

direct product	C₁₉²×C₅²⋊C₃
unambiguous semidirect product	C₅²⋊(C₃×C₁₉²)

Fitting, socle, Hall	C₅²×C₁₉² ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₁₉²

	subgroup	G/H
center, hypercenter	C₁₉²	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₁₉²
Frattini	C₁	G
Fitting, socle	C₅²×C₁₉²	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₉²

132 conjugacy classes of subgroups.

μ_t(G) = 5415

3971 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27075, 16);