Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C541 ⋊ C4 |
| Sylow | C541 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^6,541|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^52,c^b=cf,g^e=g^5401372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1560);