GL(2,𝔽₃)⋊A₄ #10596392

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

Aliases

unambiguous semidirect product	GL(2,𝔽₃)⋊A₄
unambiguous semidirect product	#5924⋊C₃

Fitting	H(5,𝔽₂) ⋊ C₃×D₃
derived	#994 ⋊ C₂×C₃

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	A₄×S₄
commutator, cosocle, hypocenter	#994	C₂×C₃
Fitting	H(5,𝔽₂)	C₃×D₃
LCS	G ▷ #994
UCS	C₁ ◁ C₂

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 32

Polycyclic presentation:

2,3,2^2,3,2^3|c^2=h,d^2=h,f^2=h,g^2=h,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,d^b=c,d^c=dh,f^e=g,g^e=fgh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8274);