#33002965

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Fitting	C₇₃×#2140 ⋊ C₂
Sylow	C₇₃ ⋊ #12999

564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

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

μ_t(G) = 2336

Polycyclic presentation:

2^8,73|a^2=f,b^2=dfg,d^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,d^c=dh,f^c=fh,i^c=i^72

1192 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 86549);