D₄₅×C₃₇₃ #46777058

order	33570
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₄₅×C₃₇₃
unambiguous semidirect product	C₅⋊(D₉×C₃₇₃)
unambiguous semidirect product	C₉⋊(D₅×C₃₇₃)

	subgroup	G/H
center, hypercenter	C₃₇₃	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₃₇₃
Frattini	C₃	D₁₅×C₃₇₃
Fitting	C₅×C₉×C₃₇₃	C₂
socle	C₃×C₅×C₃₇₃	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₃₇₃

24 conjugacy classes of subgroups.

μ_t(G) = 16785

8952 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33570, 8);