C₅×D₂₁×C₁₇₃ #49138097

order	36330
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₂₁×C₁₇₃
unambiguous semidirect product	C₃⋊(C₅×D₇×C₁₇₃)
unambiguous semidirect product	C₇⋊(C₅×D₃×C₁₇₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₇₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₅×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₇₃

32 conjugacy classes of subgroups.

μ_t(G) = 18165

10380 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36330, 12);