#16846652

order	3968
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₃₁ ⋊ #1985

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₁
commutator, socle, prime radical	C₂³×C₃₁	C₂²×C₄
Fitting	C₂×C₄×Q₈×C₃₁	C₂
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×C₄×Q₈	D₃₁
hypocenter	C₃₁	#1985
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

280 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

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

μ_t(G) = 3968

Polycyclic presentation:

2^7,31|a^2=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^30,c^b=cg,h^b=h^30

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 5451);