#36441786

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₈₉×#1318 ⋊ C₂
Sylow	C₈₉ ⋊ #7344

376 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 43 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|a^2=d,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=deh,e^b=eh,g^b=gh,i^b=i^88,d^c=dgh,e^c=eh,e^d=eh

1178 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 56926);