#11921571

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×S₄
commutator, prime radical, cosocle	C₂×C₃×SL(2,𝔽₃)	C₂³
Fitting	C₃×C₄×Q₈	C₂×D₃
socle	C₂²×C₃	C₂²×S₄
hypercenter	C₂×C₄	D₃×S₄
hypocenter	C₃×SL(2,𝔽₃)	C₂×Q₈
LCS	G ▷ C₂×C₃×SL(2,𝔽₃) ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

397 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

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

μ_t(G) = 384

Polycyclic presentation:

2^4,3^2,2^3|a^2=d,b^2=d,c^2=di,g^2=i,h^2=i,b^a=bd,c^a=cd,f^a=f^2,e^b=e^2,g^b=gh,h^b=hi,g^e=h,h^e=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155582);