D₂₄₃⋊C₃ #13090583

order	1458
isoclinism	isoclinic class of D₂₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	D₂₄₃⋊C₃
unambiguous semidirect product	(C₂₄₃⋊C₃)⋊C₂

Fitting, Sylow	C₂₄₃⋊C₃ ⋊ C₂
derived	C₂₄₃ ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₄₃	C₂×C₃
Frattini	C₈₁	C₃×D₃
Fitting	C₂₄₃⋊C₃	C₂
socle	C₃	C₃×D₈₁
LCS	G ▷ C₂₄₃
UCS	C₁

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 243
transitive degree	μ_t(G) = 243

Polycyclic presentation:

2,3^6|b^3=d,d^3=e,e^3=f,f^3=g,b^a=b^2d^2e^2f^2g^2,d^a=d^2e^2f^2g^2,e^a=e^2f^2g^2,f^a=f^2g^2,g^a=g^2,c^b=cg

maximal subgroup of	#72277482
maximal normal subgroup of	#72277482

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 657);