Finite Group DatabasebetaFinite Group Databasebeta| order | 33325 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C31⋊C25 |
| unambiguous semidirect product | C31⋊(C25×C43) |
| unambiguous semidirect product | (C31×C43)⋊C25 |
| derived, Sylow | C31 ⋊ C25×C43 |
| Hall | C31×C43 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C43 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C25×C43 |
| Frattini | C5 | C43×ΓL(1,𝔽32) |
| Fitting, socle, prime radical | C5×C31×C43 | C5 |
| cosocle | C5×C31 | C5×C43 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C43 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33325 |
2365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33325, 2);