Finite Group DatabasebetaFinite Group Databasebeta| order | 8604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C239⋊#157 |
| Fitting, socle, derived, Hall | C32×C239 ⋊ C4 |
| Sylow | C239 ⋊ #157 |
| Sylow | C32 ⋊ Dic239 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C239 | C4 |
| LCS | G ▷ C32×C239 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,239|a^2=b,c^a=cd,d^a=cd^2,e^a=e^238,c^b=c^2,d^b=d^2720 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8604, 24);