Finite Group DatabasebetaFinite Group Databasebeta| order | 32608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C1019 ⋊ C2 |
| Sylow | C1019 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D1019 |
| commutator, socle, cosocle | C22×C1019 | C23 |
| Fitting | C42×C1019 | C2 |
| hypercenter | C42 | D1019 |
| hypocenter | C1019 | #127 |
| LCS | G ▷ C22×C1019 ▷ C1019 | |
| UCS | C1 ◁ C22 ◁ C42 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16304 |
Polycyclic presentation:
2^5,1019|b^2=d,c^2=e,b^a=bd,c^a=ce,f^a=f^10188158 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32608, 143);