C₃×C₄₇×C₂²⋊(C₁₃⋊C₃) #36347276

order	21996
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₄₇×C₂²⋊(C₁₃⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₁₃⋊C₃×C₄₇)
unambiguous semidirect product	(C₃×C₁₃)⋊(A₄×C₄₇)
unambiguous semidirect product	(C₂²×C₃×C₄₇)⋊(C₁₃⋊C₃)
unambiguous semidirect product	(C₃×C₁₃×C₄₇)⋊A₄

	subgroup	G/H
center, hypercenter	C₃×C₄₇	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₄₇	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₄₇

56 conjugacy classes of subgroups.

μ_t(G) = 7332

2820 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 117);