Finite Group DatabasebetaFinite Group Databasebeta| order | 32396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D91⋊D89 |
| unambiguous semidirect product | D623⋊D13 |
| unambiguous semidirect product | D1157⋊D7 |
| Fitting, socle, derived, Hall | C7×C13×C89 ⋊ C22 |
| Hall | C13×C89 ⋊ C2×D7 |
| Hall | C7×C89 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D89 |
| Sylow | C89 ⋊ D7×D13 |
| Sylow | C13 ⋊ D7×D89 |
| Sylow | C7 ⋊ D13×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C89 | C22 |
| LCS | G ▷ C7×C13×C89 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8099 |
Polycyclic presentation:
2^2,7,13,89|d^a=d^12,e^a=e^88,c^b=c^6,d^b=d^122108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32396, 28);