#28363306

order	13952
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	#424×C₁₀₉ ⋊ C₂
Sylow	C₁₀₉ ⋊ #1866

270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

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

μ_t(G) = 3488

Polycyclic presentation:

2^7,109|a^2=f,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,e^b=eg,h^b=h^108,d^c=dg,e^c=eg,h^c=h^108

1550 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4784);