C₂₇₁⋊C₁₂₅ #46799724

order	33875
automorphism	?
homology	Abelianization (H₁) = C₁₂₅ · Schur multiplier (H₂) = C₁

Aliases

C₂₇₁⋊C₁₂₅

C₂₇₁ ⋊ C₁₂₅

	subgroup	G/H
center, Frattini, hypercenter	C₂₅	C₂₇₁⋊C₅
commutator, hypocenter	C₂₇₁	C₁₂₅
Fitting, cosocle	C₂₅×C₂₇₁	C₅
socle, prime radical	C₅×C₂₇₁	C₂₅
LCS	G ▷ C₂₇₁
UCS	C₁ ◁ C₂₅

8 conjugacy classes of subgroups.

μ_t(G) = 33875

Polycyclic presentation:

5^3,271|a^5=b,b^5=c,d^a=d^10

1475 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33875, 6);