C₇×C₉⋊(D₄₃⋊C₇) #49181536

order	37926
automorphism	?
homology	Abelianization (H₁) = C₂×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇×C₉⋊(D₄₃⋊C₇)
unambiguous semidirect product	C₉⋊(C₇×D₄₃⋊C₇)
unambiguous semidirect product	(C₄₃⋊C₇)⋊(C₇×D₉)
unambiguous semidirect product	D₃₈₇⋊C₇²
unambiguous semidirect product	(C₇×D₃₈₇)⋊C₇

	subgroup	G/H
center, hypercenter	C₇	C₉⋊(D₄₃⋊C₇)
commutator, cosocle, hypocenter	C₉×C₄₃	C₂×C₇²
Frattini	C₃	C₇×C₃⋊(D₄₃⋊C₇)
Fitting	C₇×C₉×C₄₃	C₂×C₇
socle	C₃×C₇×C₄₃	D₃×C₇
LCS	G ▷ C₉×C₄₃
UCS	C₁ ◁ C₇

120 conjugacy classes of subgroups.

μ_t(G) = 2709

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37926, 109);