#49096470

order	35968
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₈₁ ⋊ #2030

	subgroup	G/H
center	C₂²	#22582847
commutator, prime radical, cosocle	C₂⁴×C₂₈₁	C₂³
Frattini	C₂⁴	C₂²×D₂₈₁
Fitting	#381×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#120
hypercenter	#381	D₂₈₁
hypocenter	C₂₈₁	#2030
LCS	G ▷ C₂⁴×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

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

μ_t(G) = 8992

Polycyclic presentation:

2^7,281|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^280

3946 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 5677);