Finite Group DatabasebetaFinite Group Databasebeta| order | 32396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#17987774 |
| Fitting, socle, derived, Hall | C7×C13×C89 ⋊ C4 |
| Hall | C13×C89 ⋊ Dic7 |
| Hall | C7×C89 ⋊ #261 |
| Hall | C7×C13 ⋊ Dic89 |
| Sylow | C89 ⋊ C7⋊#261 |
| Sylow | C13 ⋊ Dic623 |
| Sylow | C7 ⋊ #17987774 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C89 | C4 |
| prime radical, cosocle | C7×D13×C89 | C2 |
| LCS | G ▷ C7×C13×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8099 |
Polycyclic presentation:
2^2,7,13,89|a^2=b,c^a=c^6,d^a=d^5,e^a=e^88,d^b=d^122495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32396, 22);