C₃⋊#88613 #13048425

order	1296
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂×C₃²

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₃⋊(C₃⋊S₄)
commutator, hypocenter	C₃×C₂²⋊H(3,𝔽₃)	C₄
Fitting	C₂³×C₃³	D₃
socle	C₂³×C₃²	C₃⋊D₃
prime radical, cosocle	C₂×C₃×C₂²⋊H(3,𝔽₃)	C₂
LCS	G ▷ C₃×C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

412 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

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

μ_t(G) = 36

Polycyclic presentation:

2^2,3^4,2^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,g^a=gh,e^c=ef,g^c=h,h^c=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2143);