#10822604

order	768
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	C₂×#953
commutator, prime radical, cosocle	C₂⁴×C₃	C₂⁴
Frattini	C₂⁴	C₂³×D₃
Fitting	C₃×#3458	C₂
socle	C₂²×C₃	C₂×#120
hypercenter	#3458	D₃
hypocenter	C₃	#23470
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3458

1178 conjugacy classes of subgroups; only the 275 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 275 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:

2^8,3|a^2=e,b^2=e,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,d^c=dh,i^c=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 196985);