#3532⋊C₃ #85659

order	384
isoclinism	isoclinic class of #3532⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting, Sylow	#3532 ⋊ C₃
derived	H(3,𝔽₄) ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	H(3,𝔽₄)	C₂×C₃
Frattini, socle	C₂²	C₂×C₂²⋊A₄
Fitting	#3532	C₃
LCS	G ▷ H(3,𝔽₄)
UCS	C₁

266 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 16

A minimal faithful permutation representation — 3 generators on 16 points:

(2,14,15,7,8,16)(3,9,11,12,13,10)(4,5,6);(2,10)(3,8)(7,11)(9,13)(12,14)(15,16);(1,15)(2,8)(3,7)(4,9)(5,13)(6,16)(10,14)(11,12)

Polycyclic presentation:

2,3,2^6|c^a=cgh,d^a=dg,c^b=dgh,d^b=cdh,e^b=fgh,f^b=efh,g^b=h,h^b=gh,e^c=egh,f^c=fh,e^d=eh,f^d=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18235);