Finite Group DatabasebetaFinite Group Databasebeta| order | 32301 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C97 · Schur multiplier (H2) = C3 |
| direct product | C3×C97×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C32×C97) |
| unambiguous semidirect product | (C3×C37)⋊(C3×C97) |
| Fitting, socle | C3×C37×C97 ⋊ C3 |
| derived, Sylow | C37 ⋊ C32×C97 |
| Hall | C37×C97 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C97 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C32×C97 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C97 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C97 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10767 |
4365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32301, 12);