C₇×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁) #30633495

order	16170
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₅×C₇×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₇×ΓL(1,𝔽₈))
unambiguous semidirect product	(ΓL(1,𝔽₈)×D₁₁)⋊(C₅×C₇)
unambiguous semidirect product	(C₇×AGL(1,𝔽₁₁))⋊(C₃×C₇)
unambiguous semidirect product	(C₇×ΓL(1,𝔽₈)×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₇	ΓL(1,𝔽₈)×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₇×C₁₁	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₇

80 conjugacy classes of subgroups.

μ_t(G) = 231

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

maximal subgroup of	C₇×AGL(1,𝔽₇)×AGL(1,𝔽₁₁), AGL(1,𝔽₁₁)×ΓL(1,𝔽₈)⋊D₇, D₇×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁), …
maximal normal subgroup of	C₇×AGL(1,𝔽₇)×AGL(1,𝔽₁₁), AGL(1,𝔽₁₁)×ΓL(1,𝔽₈)⋊D₇, D₇×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁), …
maximal quotient of	C₇×ΓL(1,𝔽₈)×Dic₁₁⋊C₅, C₂×C₇×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 40);