C₅×C₂₃×D₁₄₇ #46798908

order	33810
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₃×D₁₄₇
unambiguous semidirect product	C₃⋊(C₅×C₂₃×D₄₉)
unambiguous semidirect product	C₄₉⋊(C₅×D₃×C₂₃)

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₄₇
commutator, cosocle, hypocenter	C₃×C₄₉	C₂×C₅×C₂₃
Frattini	C₇	C₅×C₂₃×D₂₁
Fitting	C₃×C₅×C₂₃×C₄₉	C₂
socle	C₃×C₅×C₇×C₂₃	D₇
LCS	G ▷ C₃×C₄₉
UCS	C₁ ◁ C₅×C₂₃

48 conjugacy classes of subgroups.

μ_t(G) = 16905

8625 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 12);