D₉×C₃₁×C₆₇ #49153265

order	37386
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₃₁×C₆₇
unambiguous semidirect product	C₉⋊(C₂×C₃₁×C₆₇)

	subgroup	G/H
center, hypercenter	C₃₁×C₆₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₃₁×C₆₇
Frattini	C₃	D₃×C₃₁×C₆₇
Fitting	C₉×C₃₁×C₆₇	C₂
socle	C₃×C₃₁×C₆₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃₁×C₆₇

24 conjugacy classes of subgroups.

μ_t(G) = 18693

12462 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37386, 9);