D₅₅⋊D₁₇ #16836693

order	3740
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₅₅⋊D₁₇
unambiguous semidirect product	D₈₅⋊D₁₁
unambiguous semidirect product	D₁₈₇⋊D₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅×C₁₁×C₁₇
UCS	C₁

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 935

Polycyclic presentation:

2^2,5,11,17|d^a=d^10,e^a=e^16,c^b=c^4,d^b=d^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 39);