C₂₅₅₁⋊C₈ #35205244

order	20408
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

C₂₅₅₁⋊C₈

C₂₅₅₁ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₂₅₅₁
commutator, hypocenter	C₂₅₅₁	C₈
Fitting, cosocle	C₄×C₂₅₅₁	C₂
socle, prime radical	C₂×C₂₅₅₁	C₄
LCS	G ▷ C₂₅₅₁
UCS	C₁ ◁ C₄

8 conjugacy classes of subgroups.

μ_t(G) = 20408

Polycyclic presentation:

2^3,2551|a^2=b,b^2=c,d^a=d^2550

5108 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20408, 6);