#36703122

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

No aliases for this group.

Fitting	C₈₉×#1780 ⋊ C₂
Sylow	C₈₉ ⋊ #32887

3592 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 3592 conjugacy classes of subgroups — too many to draw. Only its 267 normal subgroups are shown.

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

μ_t(G) = 11392

Polycyclic presentation:

2^8,89|a^2=h,b^2=h,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^88,e^b=eh,i^b=i^88,d^c=dh

1988 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 318262);