C₁₂₇⋊#2104 #30640314

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂

Aliases

C₁₂₇ ⋊ #2104

	subgroup	G/H
center	C₂	C₁₂₇⋊#401
commutator, prime radical, cosocle	C₂⁴×C₁₂₇	C₂³
Frattini	C₂⁴	C₂²×D₁₂₇
Fitting	#342×C₁₂₇	C₂
socle	C₂×C₁₂₇	#401
hypercenter	#342	D₁₂₇
hypocenter	C₁₂₇	#2104
LCS	G ▷ C₂⁴×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #342

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

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

Polycyclic presentation:

2^7,127|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,f^b=fg,e^c=eg,h^c=h^126

1409 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6094);