Finite Group DatabasebetaFinite Group Databasebeta| order | 33153 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C257 · Schur multiplier (H2) = C1 |
| direct product | C43⋊C3×C257 |
| unambiguous semidirect product | C43⋊(C3×C257) |
| unambiguous semidirect product | (C43×C257)⋊C3 |
| Fitting, socle, Hall | C43×C257 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C257 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C3×C257 |
| Frattini | C1 | G |
| Fitting, socle | C43×C257 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C257 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11051 |
4369 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33153, 1);