C₂×C₇×D₉×C₁₄₉ #49176318

order	37548
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₉×C₁₄₉
unambiguous semidirect product	C₉⋊(C₂²×C₇×C₁₄₉)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₇×C₁₄₉)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₄₉	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₇×C₁₄₉
Frattini	C₃	C₂×D₃×C₇×C₁₄₉
Fitting	C₂×C₇×C₉×C₁₄₉	C₂
socle	C₂×C₃×C₇×C₁₄₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₇×C₁₄₉

60 conjugacy classes of subgroups.

μ_t(G) = 18774

12516 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37548, 37);