#45655391

order	32576
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₂²⋊C₈×C₅₀₉ ⋊ C₂
Sylow	C₅₀₉ ⋊ #450

188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

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

μ_t(G) = 8144

Polycyclic presentation:

2^6,509|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^508,d^b=df,g^b=g^508

5099 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 702);