C₃₁⋊C₆₂₅ #34084239

order	19375
automorphism	?
homology	Abelianization (H₁) = C₆₂₅ · Schur multiplier (H₂) = C₁

Aliases

C₃₁⋊C₆₂₅

C₃₁ ⋊ C₆₂₅

	subgroup	G/H
center, Frattini, hypercenter	C₁₂₅	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₆₂₅
Fitting, cosocle	C₃₁×C₁₂₅	C₅
socle, prime radical	C₅×C₃₁	C₁₂₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₂₅

10 conjugacy classes of subgroups.

μ_t(G) = 19375

Polycyclic presentation:

5^4,31|a^5=b,b^5=c,c^5=d,e^a=e^16

1375 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19375, 16);