#10624828⋊C₂ #13091269

order	1458
isoclinism	isoclinic class of #10624828⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#6869	C₂×C₃
Frattini	C₃×C₉	C₃×C₃⋊D₃
Fitting	#10624828	C₂
socle	C₃	#6895⋊C₂
prime radical	#6869⋊C₂	C₃
LCS	G ▷ #6869
UCS	C₁

97 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 27

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1343);