C₃×C₁₃⋊C₃×C₃₁₇ #49150579

order	37089
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₁₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₃⋊C₃×C₃₁₇
unambiguous semidirect product	C₁₃⋊(C₃²×C₃₁₇)
unambiguous semidirect product	(C₃×C₁₃)⋊(C₃×C₃₁₇)
unambiguous semidirect product	(C₁₃×C₃₁₇)⋊C₃²
unambiguous semidirect product	(C₃×C₁₃×C₃₁₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₃₁₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃²×C₃₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁₇	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₃₁₇

24 conjugacy classes of subgroups.

μ_t(G) = 12363

6657 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37089, 4);