#34444718

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

Aliases

No aliases for this group.

Fitting	C₇₉×#2151 ⋊ C₂
Sylow	C₇₉ ⋊ #33829

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

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

μ_t(G) = 10112

Polycyclic presentation:

2^8,79|a^2=h,b^2=h,d^2=eh,f^2=gh,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fg,g^a=gh,i^a=i^78,c^b=ce,d^b=dh,f^c=fg,g^c=gh,i^c=i^78

2224 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 326017);