#49159951

order	37504
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₉₃ ⋊ #2030

	subgroup	G/H
center	C₂²	#22627593
commutator, prime radical, cosocle	C₂⁴×C₂₉₃	C₂³
Frattini	C₂⁴	C₂²×D₂₉₃
Fitting	#543×C₂₉₃	C₂
socle	C₂²×C₂₉₃	#120
hypercenter	#543	D₂₉₃
hypocenter	C₂₉₃	#2030
LCS	G ▷ C₂⁴×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

μ_t(G) = 9376

Polycyclic presentation:

2^7,293|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^292

3238 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 5676);