Dic₆×PSU(3,𝔽₂) #13180614

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₃³ ⋊ Q₈²

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×PSU(3,𝔽₂)
commutator, prime radical, cosocle	C₂×C₃×C₃⋊D₃	C₂⁴
Fitting	C₃³×C₄	C₂×Q₈
socle	C₂×C₃³	C₂²×Q₈
hypercenter	C₄	D₃×PSU(3,𝔽₂)
hypocenter	C₃³	Q₈²
LCS	G ▷ C₂×C₃×C₃⋊D₃ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₄

474 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

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

μ_t(G) = 192

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46677);