#36443343

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

Aliases

No aliases for this group.

Fitting	C₈₉×#1271 ⋊ C₂
Sylow	C₈₉ ⋊ #7770

460 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

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

μ_t(G) = 11392

Polycyclic presentation:

2^8,89|a^2=f,b^2=h,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^88,d^b=df,e^b=eg,i^b=i^88,d^c=dg,e^c=eh,i^c=i^88

1709 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 58483);