C₈₉×C₃⋊AGL(1,𝔽₁₁) #44440346

order	29370
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×C₃⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	C₃⋊(C₈₉×AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(D₃×C₈₉)
unambiguous semidirect product	D₃₃⋊(C₅×C₈₉)
unambiguous semidirect product	(D₃₃×C₈₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₈₉	C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₈₉	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₈₉

32 conjugacy classes of subgroups.

μ_t(G) = 2937

1602 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 31);