#36526798

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Fitting	C₂×#534×C₈₉ ⋊ C₂
Sylow	C₈₉ ⋊ #18132

1654 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1654 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.

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

μ_t(G) = 2848

Polycyclic presentation:

2^8,89|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,i^a=i^88,e^b=eg,f^b=fh,e^c=eh

1973 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 141938);