C₂×C₃×D₁₇×C₈₉ #31827781

order	18156
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₁₇×C₈₉
unambiguous semidirect product	C₁₇⋊(C₂²×C₃×C₈₉)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂×C₃×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇×C₈₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₈₉

40 conjugacy classes of subgroups.

μ_t(G) = 9078

5340 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18156, 35);