#34315450

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁷

Aliases

No aliases for this group.

Fitting	C₂×#338×C₇₉ ⋊ C₂
Sylow	C₇₉ ⋊ #23434

1916 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

normal subgroups only

This group has 1916 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.

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

μ_t(G) = 2528

Polycyclic presentation:

2^8,79|e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^a=fh,i^a=i^78,c^b=cg,e^b=eh,g^b=gh,i^b=i^78,f^c=fh,g^c=gh,i^c=i^78

1762 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 196749);