Finite Group DatabasebetaFinite Group Databasebeta| order | 7620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic381 |
| unambiguous semidirect product | C3⋊(C5×Dic127) |
| unambiguous semidirect product | C127⋊(C5×Dic3) |
| derived, Hall | C3×C127 ⋊ C4×C5 |
| Hall | C3×C5×C127 ⋊ C4 |
| Hall | C5×C127 ⋊ Dic3 |
| Sylow | C127 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ Dic127 |
| Sylow | C3 ⋊ C5×Dic127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D381 |
| commutator, hypocenter | C3×C127 | C4×C5 |
| Frattini | C2 | C5×D381 |
| Fitting, socle | C2×C3×C5×C127 | C2 |
| LCS | G ▷ C3×C127 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
1920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7620, 7);