D₂₆₇₂ #19128774

order	5344
automorphism	Aut(G) order 3548416
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₂₆₇₂

Fitting	C₁₆×C₁₆₇ ⋊ C₂
Sylow	C₁₆₇ ⋊ D₁₆

28 conjugacy classes of subgroups.

Polycyclic presentation:

2^5,167|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^166,c^b=cd,d^b=de,f^b=f^166

1339 conjugacy classes. The character table is too large to display.

maximal subgroup of	D₈₀₁₆, D₁₃₃₆₀, D₁₈₇₀₄, …
maximal quotient of	D₈₀₁₆, D₁₃₃₆₀, D₁₈₇₀₄, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5344, 88);