C₃×C₇×D₅×C₁₇₃ #49138091

order	36330
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇×C₁₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₇×D₅×C₁₇₃
unambiguous semidirect product	C₅⋊(C₂×C₃×C₇×C₁₇₃)

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₇₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₇×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₇×C₁₇₃

32 conjugacy classes of subgroups.

μ_t(G) = 18165

14532 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36330, 6);