C₃×C₁₃⋊C₃×C₃₁₁ #49138583

order	36387
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₁₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₃⋊C₃×C₃₁₁
unambiguous semidirect product	C₁₃⋊(C₃²×C₃₁₁)
unambiguous semidirect product	(C₃×C₁₃)⋊(C₃×C₃₁₁)
unambiguous semidirect product	(C₁₃×C₃₁₁)⋊C₃²
unambiguous semidirect product	(C₃×C₁₃×C₃₁₁)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₃₁₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃²×C₃₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁₁	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₃₁₁

24 conjugacy classes of subgroups.

μ_t(G) = 12129

6531 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36387, 4);