#36368398

order	22144
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	C₄×C₈×C₁₇₃ ⋊ C₄
Sylow	C₁₇₃ ⋊ #1279

208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

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

μ_t(G) = 5536

Polycyclic presentation:

2^7,173|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=ef,h^a=h^80,h^d=h^172

1432 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 19345);