#36470562

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₈₉×#1833 ⋊ C₂
Sylow	C₈₉ ⋊ #12829

378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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=f,b^2=dg,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,e^b=eh,f^b=fh,d^c=dh,e^c=eg,g^c=gh,i^c=i^88

1454 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 85702);