C₃×C₇×ΓL(1,𝔽₈)×C₄₇ #35208606

order	20727
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇×C₄₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₇×ΓL(1,𝔽₈)×C₄₇
unambiguous semidirect product	C₇⋊(C₃²×C₇×C₄₇)
unambiguous semidirect product	(C₃×C₇)⋊(C₃×C₇×C₄₇)
unambiguous semidirect product	(C₇×C₄₇)⋊(C₃²×C₇)
unambiguous semidirect product	(C₃×C₇×C₄₇)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₃×C₇×C₄₇	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃²×C₇×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₄₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₇×C₄₇

56 conjugacy classes of subgroups.

μ_t(G) = 2961

4935 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20727, 11);