#30776083

order	17152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Fitting	C₆₇×#1525 ⋊ C₂
Sylow	C₆₇ ⋊ #13568

498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

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

μ_t(G) = 1072

Polycyclic presentation:

2^8,67|a^2=e,c^2=h,d^2=h,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^66,d^b=dh,e^b=ef,f^b=fh,g^b=gh,i^b=i^66,e^d=egh,f^d=fh,f^e=fh

1288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 89820);