#13108698

order	1632
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×D₁₇
commutator	C₂×C₃×C₁₇	C₂×C₈
Fitting, cosocle	C₂×C₃×C₄×C₁₇	C₂²
socle	C₂²×C₃×C₁₇	C₂×C₄
prime radical	C₂²×D₅₁	C₄
hypocenter	C₃×C₁₇	C₂²⋊C₈
LCS	G ▷ C₂×C₃×C₁₇ ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₄

100 conjugacy classes of subgroups.

μ_t(G) = 816

Polycyclic presentation:

2^5,3,17|a^2=d,b^2=cde,d^2=e,b^a=bc,g^a=g^16,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 33);