#36469402

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄²

Aliases

No aliases for this group.

Fitting	C₈₉×#1393 ⋊ C₂
Sylow	C₈₉ ⋊ #12583

826 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 151 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=e,b^2=f,c^2=h,d^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^c=i^88,e^d=eh

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84542);