C₇×C₂₃×D₁₁₁ #49088351

order	35742
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₂₃×D₁₁₁
unambiguous semidirect product	C₃⋊(C₇×C₂₃×D₃₇)
unambiguous semidirect product	C₃₇⋊(D₃×C₇×C₂₃)

	subgroup	G/H
center, hypercenter	C₇×C₂₃	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₃×C₃₇	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₇×C₂₃

32 conjugacy classes of subgroups.

μ_t(G) = 17871

9177 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 14);