#31916905

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#17986187
commutator, prime radical, cosocle	C₂²×D₄×C₇₁	C₂³
Frattini	C₂²×D₄	C₂²×D₇₁
Fitting	C₂×#354×C₇₁	C₂
socle	C₂²×C₇₁	B(4,𝔽₂)
hypercenter	C₂×#354	D₇₁
hypocenter	C₇₁	#13425
LCS	G ▷ C₂²×D₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ C₂×#354

508 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

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

μ_t(G) = 4544

Polycyclic presentation:

2^8,71|a^2=h,b^2=h,c^2=d,e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,c^b=cf,e^b=eg,i^b=i^70,e^c=eh,g^c=gh,i^c=i^70,f^e=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 89021);