C₅×C₇⋊(C₉⋊AGL(1,𝔽₁₁)) #46831472

order	34650
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×C₇⋊(C₉⋊AGL(1,𝔽₁₁))
unambiguous semidirect product	C₇⋊(C₅×C₉⋊AGL(1,𝔽₁₁))
unambiguous semidirect product	C₉⋊(C₅×C₇⋊AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₅×D₆₃)
unambiguous semidirect product	D₆₉₃⋊C₅²
unambiguous semidirect product	(C₅×D₆₉₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₅	C₇⋊(C₉⋊AGL(1,𝔽₁₁))
commutator, cosocle, hypocenter	C₇×C₉×C₁₁	C₂×C₅²
Frattini	C₃	C₅×C₃⋊(C₇⋊AGL(1,𝔽₁₁))
Fitting	C₅×C₇×C₉×C₁₁	C₂×C₅
socle	C₃×C₅×C₇×C₁₁	C₅×D₃
LCS	G ▷ C₇×C₉×C₁₁
UCS	C₁ ◁ C₅

192 conjugacy classes of subgroups.

μ_t(G) = 3465

1140 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 115);