Finite Group DatabasebetaFinite Group Databasebeta| order | 20704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C647 ⋊ C2 |
| Sylow | C647 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D647 |
| commutator, socle, cosocle | C22×C647 | C23 |
| Fitting | C24×C647 | C2 |
| hypercenter | C24 | D647 |
| hypocenter | C647 | #120 |
| LCS | G ▷ C22×C647 ▷ C647 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5176 |
Polycyclic presentation:
2^5,647|b^a=bd,c^a=ce,f^a=f^6465182 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20704, 115);