A₄×C₁₃×C₂₉⋊C₇ #44539796

order	31668
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₃×C₂₉⋊C₇
unambiguous semidirect product	C₂²⋊(C₃×C₁₃×C₂₉⋊C₇)
unambiguous semidirect product	C₂₉⋊(C₇×A₄×C₁₃)
unambiguous semidirect product	(A₄×C₂₉)⋊(C₇×C₁₃)
unambiguous semidirect product	(C₂²×C₂₉⋊C₇)⋊(C₃×C₁₃)
unambiguous semidirect product	(A₄×C₁₃×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₁₃	A₄×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂²×C₂₉	C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₂₉	C₃×C₇
LCS	G ▷ C₂²×C₂₉
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

μ_t(G) = 1508

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 91);