C₃⋊D₃×C₂₀₈₉ #49178192

order	37602
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₀₈₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₂₀₈₉
unambiguous semidirect product	C₃⋊(D₃×C₂₀₈₉)

Fitting, socle, Hall	C₃²×C₂₀₈₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₂₀₈₉

	subgroup	G/H
center, hypercenter	C₂₀₈₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₂₀₈₉
Frattini	C₁	G
Fitting, socle	C₃²×C₂₀₈₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₀₈₉

24 conjugacy classes of subgroups.

μ_t(G) = 18801

12534 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37602, 17);