C₂×C₄×(C₃⋊(C₃⋊C₈))⋊C₃ #13142406

order	1728
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

direct product	C₂×C₄×(C₃⋊(C₃⋊C₈))⋊C₃
unambiguous semidirect product	(C₂×C₄×C₃⋊(C₃⋊C₈))⋊C₃

derived	C₃² ⋊ C₂×C₃×C₄×C₈
Sylow	H(3,𝔽₃) ⋊ C₂×C₄×C₈

675 conjugacy classes of subgroups.

μ_t(G) = 576

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8469);