#36475305

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₈₉×#2222 ⋊ C₂
Sylow	C₈₉ ⋊ #13702

184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 5696

Polycyclic presentation:

2^8,89|b^2=dfh,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^a=i^88,i^b=i^88,e^c=eh

1190 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 90445);