#35316655

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₈₃×#2784 ⋊ C₂
Sylow	C₈₃ ⋊ #12129

456 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

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

μ_t(G) = 2656

Polycyclic presentation:

2^8,83|b^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,g^a=gh,i^a=i^82,c^b=ch,d^b=df,e^b=egh,d^c=dg,e^c=eh,e^d=eh

1340 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 81819);