Finite Group DatabasebetaFinite Group Databasebeta| order | 32396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic1157 |
| derived, Hall | C13×C89 ⋊ C4×C7 |
| Hall | C7×C13×C89 ⋊ C4 |
| Hall | C7×C89 ⋊ Dic13 |
| Hall | C7×C13 ⋊ Dic89 |
| Sylow | C89 ⋊ C7×Dic13 |
| Sylow | C13 ⋊ C7×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D1157 |
| commutator, hypocenter | C13×C89 | C4×C7 |
| Frattini | C2 | C7×D1157 |
| Fitting, socle, prime radical | C2×C7×C13×C89 | C2 |
| cosocle | C2×C13×C89 | C2×C7 |
| LCS | G ▷ C13×C89 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32396 |
8120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32396, 4);