#44550932

order	32128
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₂₅₁ ⋊ #1917

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₅₁
commutator, socle, prime radical	C₂³×C₂₅₁	C₂²×C₄
Fitting	#336×C₂₅₁	C₂
cosocle	C₂²×C₄×C₂₅₁	C₂³
hypercenter	#336	D₂₅₁
hypocenter	C₂₅₁	#1917
LCS	G ▷ C₂³×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

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

μ_t(G) = 32128

Polycyclic presentation:

2^7,251|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^250,c^b=cg,h^b=h^250,h^c=h^250

5044 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 5077);