#85558⋊C₃ #11921458

order	1152
isoclinism	isoclinic class of #85558⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting	H(3,𝔽₄) ⋊ C₃×D₃
derived	#5464 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#5464	C₂×C₃
Frattini, socle	C₂²	#1020⋊C₃
Fitting	H(3,𝔽₄)	C₃×D₃
LCS	G ▷ #5464
UCS	C₁

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 24

Polycyclic presentation:

2,3^2,2^6|c^a=c^2,d^a=f,e^a=g,f^a=d,g^a=e,h^a=hi,d^b=de,e^b=d,f^b=fg,g^b=f,d^c=e,e^c=de,f^c=fg,g^c=f,h^c=i,i^c=hi,f^d=fi,g^d=ghi,f^e=fh,g^e=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155469);