Finite Group DatabasebetaFinite Group Databasebeta| order | 32708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#11725130 |
| Fitting, socle, Hall | C13×C17×C37 ⋊ C4 |
| derived, Hall | C13×C17 ⋊ C4×C37 |
| Hall | C17×C37 ⋊ #261 |
| Hall | C13×C37 ⋊ #595 |
| Sylow | C17 ⋊ C37×#261 |
| Sylow | C13 ⋊ C37×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #11725130 |
| commutator, hypocenter | C13×C17 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C37 | C4 |
| prime radical | C37×D221 | C2 |
| cosocle | D221 | C2×C37 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8177 |
2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32708, 21);