#46831168

order	34624
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₂×Q₈×C₅₄₁ ⋊ C₄
Sylow	C₅₄₁ ⋊ #419

150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 8656

Polycyclic presentation:

2^6,541|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^52,c^b=cf,d^b=df,g^e=g^540

1372 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34624, 1542);