#10711536

order	768
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₃
commutator, socle, prime radical	C₂³×C₃	C₂²×C₈
Fitting	C₂×C₃×C₄⋊C₁₆	C₂
cosocle	C₂²×C₃×C₈	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₃
hypocenter	C₃	#12880
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

322 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

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

μ_t(G) = 768

Polycyclic presentation:

2^8,3|a^2=f,b^2=e,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^b=i^2,i^c=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 85917);