C₅×D₉×C₃₇₃ #46777056

order	33570
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₉×C₃₇₃
unambiguous semidirect product	C₉⋊(C₂×C₅×C₃₇₃)

	subgroup	G/H
center, hypercenter	C₅×C₃₇₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₃₇₃
Frattini	C₃	C₅×D₃×C₃₇₃
Fitting	C₅×C₉×C₃₇₃	C₂
socle	C₃×C₅×C₃₇₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₃₇₃

24 conjugacy classes of subgroups.

μ_t(G) = 16785

11190 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33570, 6);