#34070278

order	19328
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₅₁ ⋊ #2030

	subgroup	G/H
center	C₂²	#18012709
commutator, prime radical, cosocle	C₂⁴×C₁₅₁	C₂³
Frattini	C₂⁴	C₂²×D₁₅₁
Fitting	#342×C₁₅₁	C₂
socle	C₂²×C₁₅₁	#120
hypercenter	#342	D₁₅₁
hypocenter	C₁₅₁	#2030
LCS	G ▷ C₂⁴×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #342

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

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

μ_t(G) = 4832

Polycyclic presentation:

2^7,151|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^150,h^c=h^150

1676 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 5678);