(C₂×S₄)⋊(C₃⋊C₈) #11920635

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂³

Aliases

(C₂×S₄)⋊(C₃⋊C₈)

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×S₄
commutator	C₂×C₃×A₄	C₂×C₈
Fitting	C₂³×C₃×C₄	C₂×D₃
socle	C₂⁴×C₃	C₄×D₃
prime radical	C₂²×C₃×S₄	C₄
cosocle	C₂×C₃×C₄×A₄	C₂²
hypocenter	C₃×A₄	C₂²⋊C₈
LCS	G ▷ C₂×C₃×A₄ ▷ C₃×A₄
UCS	C₁ ◁ C₂×C₄

456 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

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

μ_t(G) = 144

Polycyclic presentation:

2^5,3^2,2^2|a^2=d,d^2=e,b^a=bc,g^a=g^2,f^b=f^2,h^b=hi,h^f=i,i^f=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154646);