C₈₉×D₁₆₉ #44473766

order	30082
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×D₁₆₉
unambiguous semidirect product	C₁₆₉⋊(C₂×C₈₉)

Fitting, Hall	C₈₉×C₁₆₉ ⋊ C₂
derived, Sylow	C₁₆₉ ⋊ C₂×C₈₉

	subgroup	G/H
center, hypercenter	C₈₉	D₁₆₉
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₈₉
Frattini	C₁₃	D₁₃×C₈₉
Fitting	C₈₉×C₁₆₉	C₂
socle	C₁₃×C₈₉	D₁₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₈₉

12 conjugacy classes of subgroups.

μ_t(G) = 15041

7654 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30082, 2);