#49122427

order	36224
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₈₃ ⋊ #2030

	subgroup	G/H
center	C₂²	#22583579
commutator, prime radical, cosocle	C₂⁴×C₂₈₃	C₂³
Frattini	C₂⁴	C₂²×D₂₈₃
Fitting	#543×C₂₈₃	C₂
socle	C₂²×C₂₈₃	#120
hypercenter	#543	D₂₈₃
hypocenter	C₂₈₃	#2030
LCS	G ▷ C₂⁴×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

μ_t(G) = 9056

Polycyclic presentation:

2^7,283|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^c=h^282

3128 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 5676);