#34315710

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Fitting	C₇₉×#3458 ⋊ C₂
Sylow	C₇₉ ⋊ #23474

1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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,b^2=e,d^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,g^b=gh,e^c=eh,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, 197009);