#10624526⋊C₂ #13090575

order	1458
isoclinism	isoclinic class of #10624526⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₃

Aliases

Fitting, Sylow	#10624526 ⋊ C₂
derived	C₃²×C₂₇ ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×C₂₇	C₂×C₃
Frattini	C₃²×C₉	C₃×D₃
Fitting	#10624526	C₂
socle	C₃	#92180
LCS	G ▷ C₃²×C₂₇
UCS	C₁

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 81

Polycyclic presentation:

2,3^6|b^3=e,d^3=g^2,e^3=g,b^a=b^2c^2d^2e^2,d^a=d^2g,e^a=e^2g^2,f^a=f^2,g^a=g^2,c^b=cd,d^b=df,f^b=fg,d^c=df,f^c=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 649);