C₂×(C₃⋊D₃)⋊(C₂²⋊A₄) #13180099

order	1728
isoclinism	isoclinic class of (C₃⋊D₃)⋊(C₂²⋊A₄)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

direct product	C₂×(C₃⋊D₃)⋊(C₂²⋊A₄)
unambiguous semidirect product	(C₂×C₃⋊D₃)⋊(C₂²⋊A₄)

Fitting	C₂⁵×C₃² ⋊ C₂×C₃
derived	C₂⁴×C₃² ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂	(C₃⋊D₃)⋊(C₂²⋊A₄)
commutator, cosocle, hypocenter	C₂⁴×C₃²	C₂²×C₃
Frattini	C₃	C₂×D₃×C₂²⋊A₄
Fitting	C₂⁵×C₃²	C₂×C₃
socle	C₂⁵×C₃	C₃×D₃
LCS	G ▷ C₂⁴×C₃²
UCS	C₁ ◁ C₂

5853 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 5853 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46162);