Finite Group DatabasebetaFinite Group Databasebeta| order | 24896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C389 ⋊ C4 |
| Sylow | C389 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3112 |
Polycyclic presentation:
2^6,389|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^274,g^b=g^115,g^d=g^388,g^e=g^388998 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24896, 1421);