Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C337 ⋊ C4 |
| Sylow | C337 ⋊ #376 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
Polycyclic presentation:
2^6,337|a^2=e,b^2=f,c^2=d,b^a=bd,g^a=g^148,g^e=g^3361384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1485);