#35314633

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₂×C₂²⋊C₁₆×C₈₃ ⋊ C₂
Sylow	C₈₃ ⋊ #11703

466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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|a^2=e,c^2=h,d^2=gh,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^82,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^82

3338 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 79797);