D₂₆₉₅ #19129125

order	5390
automorphism	Aut(G) order 4527600
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₆₉₅
unambiguous semidirect product	C₅⋊D₅₃₉
unambiguous semidirect product	C₁₁⋊D₂₄₅
unambiguous semidirect product	C₄₉⋊D₅₅

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₁₁×C₄₉	C₂
Frattini	C₇	D₃₈₅
socle	C₅×C₇×C₁₁	D₇
LCS	G ▷ C₅×C₁₁×C₄₉
UCS	C₁

24 conjugacy classes of subgroups.

Polycyclic presentation:

2,5,7,11,7|c^7=e^6,b^a=b^4,c^a=c^6e,d^a=d^10,e^a=e^6

1349 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5390, 12);