Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C49×C73 ⋊ C9 |
| Sylow | C73 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ #10620321 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24924354 |
| commutator, hypocenter | C49×C73 | C9 |
| Frattini | C3×C7 | #13095275 |
| Fitting, cosocle | C3×C49×C73 | C3 |
| socle, prime radical | C3×C7×C73 | ΓL(1,𝔽8) |
| LCS | G ▷ C49×C73 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32193 |
Polycyclic presentation:
3,7,73,3,7|a^3=d,b^7=e^2,b^a=b^2e,c^a=c^8,e^a=e^23585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 4);