#44507170

order	30848
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Fitting	#341×C₂₄₁ ⋊ C₂
Sylow	C₂₄₁ ⋊ #1738

372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.

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

μ_t(G) = 7712

Polycyclic presentation:

2^7,241|a^2=e,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^240

3404 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 4235);