C₃×C₇₁×C₄₉⋊C₃ #44531146

order	31311
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₇₁×C₄₉⋊C₃
unambiguous semidirect product	C₄₉⋊(C₃²×C₇₁)
unambiguous semidirect product	(C₃×C₄₉)⋊(C₃×C₇₁)
unambiguous semidirect product	(C₄₉×C₇₁)⋊C₃²
unambiguous semidirect product	(C₃×C₄₉×C₇₁)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₇₁	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₃²×C₇₁
Frattini	C₇	C₃×ΓL(1,𝔽₈)×C₇₁
Fitting	C₃×C₄₉×C₇₁	C₃
socle	C₃×C₇×C₇₁	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₇₁

36 conjugacy classes of subgroups.

μ_t(G) = 10437

4047 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31311, 6);