D₃₁₂₅ #20262156

order	6250
automorphism	Aut(G) order 7812500
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₃₁₂₅
unambiguous semidirect product	C₃₁₂₅⋊C₂

C₃₁₂₅ ⋊ C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃₁₂₅	C₂
Frattini	C₆₂₅	D₅
socle	C₅	D₆₂₅
LCS	G ▷ C₃₁₂₅
UCS	C₁

12 conjugacy classes of subgroups.

Polycyclic presentation:

2,5^5|b^5=c,c^5=d,d^5=e,e^5=f,b^a=b^4c^4d^4e^4f^4,c^a=c^4d^4e^4f^4,d^a=d^4e^4f^4,e^a=e^4f^4,f^a=f^4

1564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6250, 78);