#11808978

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂×C₄	C₂×PSU(3,𝔽₂)
commutator, prime radical, cosocle	C₂²×C₃⋊D₃	C₂⁴
Frattini	C₂²	C₂²×PSU(3,𝔽₂)
Fitting	C₃²×C₄²	Q₈
socle	C₂²×C₃²	C₂²×Q₈
hypercenter	C₄²	PSU(3,𝔽₂)
hypocenter	C₃²	#2402
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

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

μ_t(G) = 192

Polycyclic presentation:

2^7,3^2|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^2i^2,i^a=h^2i,c^b=cg,h^b=hi,i^b=hi^2,h^c=i^2,i^c=h,h^f=h^2,i^f=i^2,h^g=h^2,i^g=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 42989);