#2863⋊C₉ #11919511

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center	C₂×C₃	C₂×#126⋊C₃
commutator	C₂×C₄²	C₂²×C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²×A₄
Fitting	C₃×#2863	C₃
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₃×C₄	#126⋊C₃
hypocenter	C₄²	Q₈×C₉
LCS	G ▷ C₂×C₄² ▷ C₄²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

2^2,3,2,3,2^4|a^2=d,b^2=d,c^3=e,f^2=i,g^2=h,b^a=bd,c^a=ch,f^a=fhi,g^a=gi,f^c=gi,g^c=fg,h^c=hi,i^c=h

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153522);