#34318797

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Fitting	C₇₉×#1747 ⋊ C₂
Sylow	C₇₉ ⋊ #23794

930 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 191 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|a^2=e,d^2=ef,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^78,i^c=i^78

1768 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 200096);