#46825740

order	34432
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Fitting	C₄⋊C₈×C₂₆₉ ⋊ C₄
Sylow	C₂₆₉ ⋊ #1286

156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 8608

Polycyclic presentation:

2^7,269|a^2=d,b^2=e,c^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^82,d^b=dg,h^b=h^187,h^d=h^268,h^e=h^268

1372 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 19365);