Finite Group DatabasebetaFinite Group Databasebeta| order | 38612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#11716161 |
| Fitting, derived, Hall | C49×C197 ⋊ C4 |
| Sylow | C197 ⋊ Dic49 |
| Sylow | C49 ⋊ #11716161 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C197 | C4 |
| Frattini | C7 | C7⋊#11716161 |
| socle | C7×C197 | Dic7 |
| prime radical | C7×D197 | D7 |
| cosocle | C49×D197 | C2 |
| LCS | G ▷ C49×C197 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,197,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^183,e^a=e^6,d^b=d^1962453 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38612, 12);