Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×#568×C79 ⋊ C2 |
| Sylow | C79 ⋊ #63090 |
10836 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|f^2=h,g^2=h,b^a=bg,e^a=eh,g^a=gh,i^a=i^78,g^b=gh,i^b=i^78,d^c=dh2734 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1083424);