#30636944

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Fitting	Q₆₄×C₁₂₇ ⋊ C₂
Sylow	C₁₂₇ ⋊ SD₁₂₈

38 conjugacy classes of subgroups.

Polycyclic presentation:

2^7,127|a^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^126

1232 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2724);