#44558747

order	32128
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₅₁ ⋊ #2863

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₅₁
commutator, socle, prime radical, cosocle	C₂³×C₂₅₁	C₂⁴
Fitting	C₄³×C₂₅₁	C₂
hypercenter	C₄³	D₂₅₁
hypocenter	C₂₅₁	#2863
LCS	G ▷ C₂³×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₄³

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^250

8044 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 12892);