#5934⋊C₃ #10596395

order	576
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting	H(5,𝔽₂) ⋊ C₃×D₃
derived	#997 ⋊ C₂×C₃

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	#1020⋊C₃
commutator, cosocle, hypocenter	#997	C₂×C₃
Fitting	H(5,𝔽₂)	C₃×D₃
LCS	G ▷ #997
UCS	C₁ ◁ C₂

76 conjugacy classes of subgroups.

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

Polycyclic presentation:

2,3^2,2^5|d^2=h,e^2=h,f^2=h,g^2=h,c^a=c^2,d^a=fh,e^a=gh,f^a=dh,g^a=eh,d^b=deh,e^b=d,f^b=fg,g^b=f,d^c=e,e^c=deh,f^c=fg,g^c=f,e^d=eh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8277);