#38767968

order	25472
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	D₄⋊C₈×C₁₉₉ ⋊ C₂
Sylow	C₁₉₉ ⋊ #1629

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

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

μ_t(G) = 6368

Polycyclic presentation:

2^7,199|a^2=f,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^198,d^b=df,e^b=eg,h^b=h^198,d^c=dg,e^c=eg

2798 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 3628);