#46812498

order	34432
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₂²×C₁₆×C₂₆₉ ⋊ C₂
Sylow	C₂₆₉ ⋊ #2113

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

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

μ_t(G) = 17216

Polycyclic presentation:

2^7,269|a^2=e,e^2=f,f^2=g,b^a=bd,c^b=cg,h^b=h^268

8632 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6123);