Q₈×#6308 #13179691

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴×C₃³

Aliases

C₃³ ⋊ Q₈²

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, prime radical, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₄×Q₈	C₂
hypercenter	C₄×Q₈	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	Q₈²
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

2968 conjugacy classes of subgroups; only the 955 normal subgroups are shown.

normal subgroups only

This group has 2968 conjugacy classes of subgroups — too many to draw. Only its 955 normal subgroups are shown.

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

μ_t(G) = 1728

285 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 45754);