Finite Group DatabasebetaFinite Group Databasebeta| order | 15633 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C193 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C193⋊C3 |
| commutator, socle, cosocle | C3×C193 | C33 |
| Fitting, prime radical | H(3,𝔽3)×C193 | C3 |
| hypercenter | H(3,𝔽3) | C193⋊C3 |
| hypocenter | C193 | #737 |
| LCS | G ▷ C3×C193 ▷ C193 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5211 |
Polycyclic presentation:
3^4,193|c^3=d,b^a=bd,e^c=e^84737 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15633, 46);