#34219313

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³×C₄³

Aliases

No aliases for this group.

Fitting	C₇₉×#1446 ⋊ C₂
Sylow	C₇₉ ⋊ #14662

1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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=ef,b^2=h,d^2=e,b^a=be,c^a=cf,i^a=i^78,c^b=cg,d^b=def,d^c=de,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, 100612);