#30642035

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₂₇ ⋊ #2402

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₂₇
commutator, socle, prime radical, cosocle	C₂³×C₁₂₇	C₂⁴
Frattini	C₂³	C₂³×D₁₂₇
Fitting	#376×C₁₂₇	C₂
hypercenter	#376	D₁₂₇
hypocenter	C₁₂₇	#2402
LCS	G ▷ C₂³×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^126

2564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 7815);