#35316464

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

Aliases

No aliases for this group.

Fitting	C₈₃×#1317 ⋊ C₂
Sylow	C₈₃ ⋊ #12095

458 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

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

μ_t(G) = 5312

Polycyclic presentation:

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

1091 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 81628);