#36468211

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

Aliases

No aliases for this group.

Fitting	C₈₉×#1331 ⋊ C₂
Sylow	C₈₉ ⋊ #12368

424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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|a^2=g,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^88,d^b=df,e^b=eg,f^b=fh,i^b=i^88,d^c=dg,e^c=eg,i^c=i^88

1976 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 83351);