C₅×C₆₁×D₅₁ #44527441

order	31110
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₆₁×D₅₁
unambiguous semidirect product	C₃⋊(C₅×D₁₇×C₆₁)
unambiguous semidirect product	C₁₇⋊(C₅×D₃×C₆₁)

	subgroup	G/H
center, hypercenter	C₅×C₆₁	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₅×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₆₁	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅×C₆₁

32 conjugacy classes of subgroups.

μ_t(G) = 15555

8235 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 14);